Q1 Module 1 Physics 1 vector and measurement_021930.pdf

SPECIALIZED SUBJECT - STEM GENERAL PHYSICS 1 ___ SEMESTER, SY ______ QUARTER 1, MODULE 1 MEASUREMENTS AND VECTORS General Physics 1 Self-Learning Modules ___ SEMESTER, SY ____ Quarter 1 – Module 1: Vectors and Measurements First Edition, 2021 Republic Act 829...

SPECIALIZED SUBJECT - STEM GENERAL PHYSICS 1 ___ SEMESTER, SY ______ QUARTER 1, MODULE 1 MEASUREMENTS AND VECTORS General Physics 1 Self-Learning Modules ___ SEMESTER, SY ____ Quarter 1 – Module 1: Vectors and Measurements First Edition, 2021 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Published by the Division of Romblon Superintendent: Maria Luisa D. Servando, Ph.D, CESO VI OIC-Asst. Superintendent: Mabel F. Musa, Ph.D., CESE DEVELOPMENT TEAM OF THE MODULE Writers: Ryan M. Alvarez Klenly F. Dela Peña Henry S. Visca Marife M. Osorio Evaluator: Lyndie Pearl Mińano Illustrator: Mario Johray V. Manongdo Layout Artist: Mario Johray V. Manongdo Management Team: Erwin M. Marquez Johanie T. Andres Division Management Team: Maria Luisa D. Servando, Ph.D., CESO VI Mabel F. Musa, Ph.D., CESE Melchor M. Famorcan, Ph.D. Apryl C. Bagnate Ruben R. Dela Vega Leopoldo M. Mago Jr. Leona Lynn F. Famorcan Printed in the Philippines by Department of Education MIMAROPA Region Schools Division of Romblon Office Address : Brgy. Capaclan, Romblon, Romblon Telefax : E-mail Address : [email protected]  LESSON Measurement: Units, Conversion, 1 and Scientific Notation Introduction Hi Senior High School, in this lesson you will learn to: 1. Solve measurement problems involving conversion of units and expression of measurements in scientific notation; 2. Differentiate accuracy from precision; and 3. Differentiate random errors from systematic errors. Can you accurately calculate the distance you covered from home to school? To market? Or from any point of origin to wherever destination you want to go? The difference between mass, weight and height in different units? The exact speed and acceleration of large vessels and other means of transportation expressed in different units of measurement? These are some of the situations that come along our way in everyday life. To understand it deeply, let this module introduce and explain the concept of this lesson. LESSON AND PRACTICE EXERCISES DISCUSSION OF LESSON Measurement is a process of comparing an unknown quantity with some standard quantity of equal nature. Measurement of an object consists of: (1) the unit of measurement and (2) the number of units the object measures. Measurement unit is a standard quantity used to express a physical quantity. In measuring, we need standard unit of measurement to make our judgment more reliable and accurate. For proper dealing, measurement should be the same for everybody. Thus, there should be uniformity in measurement. For the sake of uniformity, we need a common set of units of measurement, which we called standard units. Standard unit of Measurement are commonly used units of measurement, which helps us measure length, height, weight, temperature, mass and more. The different system of units for measurement of physical quantities are C.G.S (centimeter, gram and the second) or known as Metric system, and the F.P.S (foot, pound, second) or known as British system. The metric system is the measurement system which is internationally accepted. This is also known as SI (International System) units of measurement. According to this system, there are seven basic or fundamental units:  the meter (m) for length  The kilogram (kg) for mass   The second (s) for time  The Kelvin (K) for temperature  The ampere (A) for electric current  The candela (cd) for luminous intensity  The mole (mol) for the amount of substance Conversion of Units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors, a number used to change one set of units to another by multiplying or dividing. Proper hand washing suggests 30 seconds rubbing both hands with soap and water to effectively remove germs and bacteria. How many minutes equivalent is 30 seconds? How important is checking your body temperature nowadays? The normal body temperature is 37o Celsius, what is its equivalent in Kelvin Scale? Here’s an example of conversion table: UNIT Equivalent Units 1 cm 0.3937 in 1 in 2.54 cm 1m 39.37 cm 1m 3.28 ft 1 mile 5280 ft 1 mile 1.609 km 1 kilogram 2.205 lb 1 pound 453.6 g 1 ton (metric) 2205 lb 1 ton (british) 2000 lb 1 pound 16 ounces (oz) Example: 1. The distance between the Sta. Fe National High School-JHS and Sta. Fe National High School-SHS is 200 meters(m). Find its distance in kilometer (km). Remember the conversion factor 1 kilometer = 1 000 meters. Note: 1 kilometer = 1 000 meters 1 𝐾𝑖𝑙𝑜𝑚𝑒𝑡𝑒𝑟 200 meter = = 0.2 Kilometer 1 000 𝑚𝑒𝑡𝑒𝑟 Note that the meter unit is being cancelled, therefore the answer is in kilometer. 2. A certain angler from Santa Fe, Romblon caught a Pugok in Agmanic reef weighing 45 kilograms (kg). What is its equivalent weight in pounds (lb)? Note: 1 kilogram = 2.205 pounds 2.205 𝑝𝑜𝑢𝑛𝑑𝑠 45 kilograms = = 99.225 pounds / 99.23 lb 1 𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚 Standard Notation is the standard way of writing numbers. For example, five hundred ninety can be written as 590. Scientific Notation on the other hand which is also called exponential notation is a convenient way of writing values using the power of ten notations wherein we can determine the number of significant digits as well as the place value of the digit. Significant figure refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation. FIVE (5) RULES FOR SIGNIFICANT FIGURES 1. All non-zero (numbers from 1-9) numbers are significant. Example: 38.5 g has 3 significant figures. 29 kg has 2 significant figures 2. Zeros between non-zero digits (middle zeroes) are significant. Example: 5007 m has 4 significant figures. 20.009 has 5 significant figures 3. Leading zeros (zeros that appear in front of the nonzero digits) are not significant. Example: 0.000087 cm has 2 significant figures 0.00604 m has 3 significant figures 4. Trailing zeros (zeros that appear after all nonzero digits) to the right of the decimal are significant. Example: 98.00 km has 4 significant figures 6.0 m has 2 significant figures 5. Trailing zeros in a whole number with no decimal shown are not significant. Example: 5 000 s has 1 significant figure 67 000 has 2 significant figures Changing Standard Notation to Scientific Notation: STANDARD NOTATION SCIENTIFIC NOTATION  560 000 000 5.6 x 108 0.00000094 9.4 x 10-7 Rule: If the decimal is moved to the left, the exponent will be positive. If the decimal is moved to the right, the exponent will be negative. Changing Scientific Notation to Standard Notation: SCIENTIFIC NOTATION STANDARD NOTATION 3.8 x 10-4 0.00038 2.09 x 105 209 000 Rule: If the exponent is positive, move the decimal point to the right. Annex zeroes where it is needed. If the exponent is negative, move the decimal point to the left. Add zeroes where it is needed. ACCURACY AND PRECISION What do you think is more important? An instrument that record accurate measurements or the one that record the precise measurements? Accuracy refers to how close a measured value is to an accepted value while precision refers to how close together a series of measurements are to each other. A classic way of demonstrating the difference between precision and accuracy is with a dartboard. Study the given figure below. Think of the bulls-eye (center) of the dartboard as the accepted value. Each dart represents the repeated measurement of the same quantity. Try to describe each figure by choosing its description below. Write your answer on your answer sheet. Precise and Accurate Neither precise nor accurate Accurate but not precise Precise but not accurate 1. ___________ 3. ___________ 4 2. ___________ 4. ___________ A measurement is reliable if it is accurate as well as precise. Accuracy and precision are both important if you want to measure anything and to make measurements you need some sorts of instruments. Below are some examples of instruments used for accurate measure. A Vernier caliper allows to measure length including outside dimensions, inside dimensions and depth of smaller objects with more precision and accuracy. It can measure up to or decimal place in which makes it good to use in small and precise measurements. Micrometer is used to make accurate measurements of the thickness of a sheet of paper and the external diameter of thin wires. It can measure up to or decimal place in.  All measurements have a degree of uncertainty regardless of precision and accuracy. Uncertainty in measurement is the doubt that exists about the result of any measurement. This is the amount by which the measurement can be more or less than the original value. This is caused by two factors. The random errors and the systematic errors. Random errors are a matter of pure chance. It usually happens because of environmental factors and slight variations in procedure. For example, when weighing yourself on a scale, you position yourself slightly different each time. Systematic errors on the other hand refers to some flaw in an instrument and procedure which will affect the reading consistently. It includes observational error, imperfect instrument calibration, and environmental interference. For example, forgetting to zero a balance produces mass measurements that are always “off” the same amount. PRACTICE EXERCISES PRACTICE EXERCISE 1 (Measurement) Direction: Select the unit of measurement that can be used to describe the given material or event. Write your answer on the separate sheet of paper. 1. Average height of a human (second, centimeter, grams) 2. Duration in charging cellphones (hours, meter, centigrams) 3. Medicinal dosage (kilogram, gram, milligram) 4. Information response through the use of internet in (hours, minutes, seconds) your locality 5. Thickness of your 1st Quarter module (meter, centimeter, feet) 6. Weight of a new-born child (kilogram, minutes, centimeter) 7. Standard weight of Lazada parcel (candela, gram, Kelvin) 8. Time travel from San Agustin Port to Romblon Port (hours, Celsius, meter) 9. Bridge capacity in Tablas provincial road (tons, kilogram, gram) 10. Length of time to finish answering your (hours, gram, meter) Physics Module PRACTICE EXERCISE 2 (Conversion Factor) Direction: Use the conversion factor given to solve the following problems. Write your answer with complete solution on the answer sheet provided. 1. How many inches are there in 5 meters? 1 meter = 39.4 inches 2. 8 000 000 milligrams is equivalent to how many kilograms? Express your answer in scientific notation. 1 kilogram = 1 000 grams 1 gram = 1 000 milligrams PRACTICE EXERCISE 3 (Significant Figures) A. Direction: Determine the number of significant figures in each of the following. ____________1. 800 000 ____________4. 54.000 ____________2. 986 ____________5. 4 006 ____________3. 0.000034 (Scientific Notation) B. Direction: Complete the table. STANDARD NOTATION EXPONENTIAL NOTATION 1.) 8.23 x 10-2 934 000 000 000 2.) 3.) 6.1 x 106 4.) 2.15 x 10-4 6 000 5.)  Instruction: Please write your learning from the above discussion. Write your learning in your notebook/answer sheet. Upon reading the lesson above, I learned that ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ and realized that ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ LESSON Vectors and Addition 2 of Vectors INTRODUCTION Hello Senior High! In this lesson you will learn to: 1. Differentiate vector and scalar quantities; 2. Perform addition of vectors; 3. Rewrite a vector in component form; and 4. Display awareness of the uses of vectors in different fields like technology and engineering. Did you know? Most of the time we are confused between speed and velocity. We thought that the two terms are the same and interchangeable but technically speaking the speed of an object is the magnitude of the change of its position while velocity of an object is the rate (magnitude) of change of its position and in what direction. LESSON AND PRACTICES DISCUSSION OF LESSON Speed and velocity are examples of quantities such as scalar quantity and vector quantity. The table below tells us the difference between scalar and vector: Scalar Quantity Vector Quantity  Only has magnitude  Has magnitude and direction Speed has magnitude (size) but no To fully describe the motion an object, direction. you must describe both the magnitude (size or numerical value) and the direction.   Only one dimensional  It is multidimensional 3  | | | | | 2 1 1 2 3 4 5 0  | | | | | | | | | | -3 -2 -1 -1 0 1 2 3 1 2 3 4 5 6 7 8 9 10 -2 -3 Just like a number line. Just like a number plane.  This quantity changes with the  This quantity changes with change in magnitude magnitude and direction A person’s weight is heavier on Earth than on the Moon. There is a big An increase in the magnitude of the difference between the gravitational pull temperature changes its quantity. of two heavenly bodies. Examples of Scalar and Vector Quantities SCALARS VECTORS Symbol Name Example Symbol Name Example d Distance 20 m d Displacement 20 m north v Speed 45 m/s v Velocity 45 m/s west m Mass 60 kg W Weight 600 kg.m/s2 (N) E Energy 400 J a Acceleration 60m/s2 down g ρ Density 14 Force 30 N up cm 3 F P Power 108 W I Impulse 20 N/s Length, Area, l, a, v 5 m, 5 m2, 5cm3 P Pressure 100 psi Volume t Time 15 s p Momentum 250 Kg m/s east T Temperature 40̊C G Gravity 9.8 m/s2 down W Work 35 N m D Drag 300 N up Vector Representation Vectors can be represented by the use of an arrow with a head and a tail. The length of the arrow represents the magnitude of the vector while the direction of the arrowhead represents the direction of the vector. The tail is called the initial point or the origin of the vector. Parts of vector diagram Vector direction can be due East, due West, due South or due North. However, some vectors do not lie exactly on the axis and are projected to a certain degree. This kind of vector can be drawn a. Geographical b. vector by moving the given degrees from the direction using inclined at compass reference axis. Example: 30̊ North an angle The magnitude of a vector in a scaled SCALE: 1 cm = 4 miles vector diagram is shown by the length of the arrow with a chosen scale. Example: The diagram shows a vector d = 20 mi with a magnitude of 20 miles. Since the scale used for constructing the diagram 600 is 1 cm = 5 miles, the vector arrow is drawn with a length of 4 cm. That is, 4 cm x (5 miles / 1 centimeter) = 20 miles. Scaled Vector Diagram Addition of Vectors Vectors can be added graphically or analytically. The vector sum is called the resultant vectors. The vectors added are called the components vectors. The head-to-tail method is a graphical way to add vectors. The tail of the vector is the starting point of the vector, and the head (or tip) of a vector is the final, pointed end of the arrow. Graphical Method Addition of Vectors Graphically  Choose an appropriate scale and frame of reference for the given vectors.  Draw the first vector starting from the frame of reference.  Draw the second vector from the head of the first vector. And draw the remaining vectors from the head of the most recent vector drawn. It must be connected in the head-to-tail method.  Draw a new vector connecting the tail of the first vector to the head of the last vector drawn. This will be the resultant vector. Example 1: A student drives his car 6.0 km, North before making a right hand turn and driving 6.0 km to the East. Finally, the student makes a left hand turn and travels another 2.0 km to the North. What is the magnitude of the overall displacement of the student? (Scale 2mm:1km) Step 1. Draw the diagram of the vectors given. + + = ? 6.0 km, North 6.0 km, East 2.0 km, North Step 2. Add the three vectors (arrows) in head-to-tail fashion.  Step 3. Draw the arrow of the Resultant. The Resultant is a vector that extends from the tail of the first vector (6.0 km, North, shown in blue) to the arrow head of the last vector (2.0 km, North, shown in green). 2.0 km, N 6.0 km, E 6.0 km, N Resultant Step 4. Measure the resultant using the foot rule. R= 15 km PRACTICE EXERCISES Practice Exercise A (Graphical Method): Juan and Anne are doing the Vector Walk Lab. Starting the door of their Science classroom, they walk 2 m, south. They make a right hand turn and walk 1.6 m, west. They turn right again and walk 24 m, north. They then turn left and walk 36 m, west. What is the resultant vector? Analytical Method Analytical methods of vector addition employ geometry and simple trigonometry rather than the ruler and protractor of graphical methods. Part of the graphical technique is retained, because vectors are still represented by arrows for easy visualization. However, analytical methods are more concise, accurate, and precise than graphical methods, which are limited by the accuracy with which a drawing can be made. Analytical methods are limited only by the accuracy and precision with which physical quantities are known.  Addition of Vectors Analytically  Vectors in the same or opposite direction on the same plane – add algebraically and use sign convention; North & East positive; South & West negative.  Vectors perpendicular or in right-angle – use the Pythagorean Theorem (the square of the hypotenuse is equal to the sum of the square of two other sides) for the magnitude and use trigonometric functions for the direction.  Vectors not perpendicular – use the law of cosine (the square of one side is equal to the sum of the square of two other sides minus twice their product multiplied by the cosine of their included angle) for a 2  b2  c 2  2bc cos A the magnitude and the law of sine (the sine of any b2  a 2  c 2  2ac cos B angle is directly proportional to the length c 2  a 2  b2  2ab cosC of the sides) for the direction. Y- The component method is a more axis convenient and accurate way to add vectors. In this method the x and y components of each vector are determined. The x component is the projection of the vector on the x-axis Origin and the y component is the projection on the y-axis. X-axis Projection of Vector Example 2 (Analytical-Pythagorean Theorem): Eric leaves his home going to the town 11km, north and then went to market 3 km, east. What is Erics’ displacement (resultant)? Step 1: Draw the diagram of the vectors given. + = ? 11 km, North 3.0 km, East Step 2. Add the two vectors (arrows) in head-to-tail fashion. Step 3. Draw the arrow of the Resultant. The Resultant is a vector that extends from the tail of the first vector (6.0 km, North, shown in blue) to the arrow head of the last vector (3.0 km. East, shown in red). a b c (resultant) Since the northward displacement and the eastward displacement are at right angles to each other, the Pythagorean Theorem can be used to determine the resultant. Step 4. Calculate the resultant using the Pythagorean Theorem Given: a= 3.0 km Solution: b= 6.0 km c2 = 3 km2 + 6 km2 = 9 km2 + 36 km2 c=? = 45 km2 = √ 45 km2 = 6.7 km NE (resultant)  PRACTICE EXERCISES Practice Exercise B: Direction: Use the Pythagorean Theorem to find the resultant magnitude for the following vectors. 1. You move at 3 m/s directly north, then 5 m/s directly west. 2. You pull down the rope with a force of 24N, then to the right with a pull force of 12 N Example 3: (Analytical- Component Method) An airplane in Tugdan Airport travels 209 km on a straight course at an angle of 22.5o north of east. It then changes its course by moving 100km north before reaching its destination. Determine the resultant displacement of the airplane. Given: d1 = 209 km Ө = 22.5o d2= 100 km Step 1. Draw the first vector then find the x and y component of the vector. y Ө= 22.5o x Let’s find the x-component of d1. Notice that the x-component is adjacent to the angle of 22.5o, so, we will use the cosine function. cos Ө = adjacent = d1x hypotenuse d1 d1x = d1 cos Ө = 209 km (cos 22.5o) = 209 km (.92) d1x = 192.28 km NOTE: Using trigonometry like this will not tell us the sign, (+ or -), of this component, (or any other). So, we must check the diagram for positive or negative directions. This x- component is aimed to the right, so, it is positive. Let’s find the y-component of d1. Notice that the y-component is opposite to the angle of 22.5o, so, we will use the sine function. sine Ө = opposite = d1y hypotenuse d1  d1y = d1 sine Ө = 209 km (sine 22.5o) = 209 km (.38) d1y = 79.42 km Again, check the diagram for positive or negative directions. The y-component aims up, so, it is positive. Step 2. Draw the second vector then find the x and y component of the vector. y d2 = 100km x Let’s find the x-component of d2. In this case, since the d2 lies along the y-axis, there is no x-component. d2x = 0 d2y = 100 km (because the d2 lies along the y-axis) Step 3. Add all the x-components, add all the y-components, but do not add an x- to y- component. Displacement x-component y-component D1 192.28 km 79.42 km D2 0 100 km Sum Ʃ dx =192.28 km Ʃ dy =179.42 km Step 4. Use the Pythagorean Theorem to get the magnitude of the total displacement. dR2 = (Ʃ dx)2 + (Ʃ dy)2 = √ (192.28 km) 2 + (179.42 km)2 = √ 36,864 km2 32191.5 km2 = √ 69055.5 km2 dR = 262.78 km Step 5. Use the arctangent function to get the angle. Ө = tan-1 Ʃdy Ʃdx FINAL ANSWER : -1 = tan 179.42km dR = 262.78 km, 43.01o north of east 192.28km = tan -1.933 Ө = 43.01 o PRACTICE EXERCISES PRACTICE EXERCISE 2 A. A jeep travel from Brgy. Agpanabat to town 20 km/s north west, then 32 km/s at 45o south. Determine the resultant displacement using the component method. Show your complete solution. PRACTICE EXERCISE 3 “Do the Honor, Just Name them Scalar or Vector” Directions: Determine if the following scenarios represent a scalar or vector quantity. Write your first name if it is scalar and your last name if it is vector. 1. The football player was running 10 miles an hour towards North. 2. A cyclist with a speed of 45km per hour is heading South. 3. The volume of that box at the west side of the building is 14 cubic feet. 4. The distance from my house to school is 3,000 meters. 5. The temperature of the room was 15 degrees Celsius. 6. The car accelerated north at a rate of 4 meters per second squared. 7. Mike burned 4000 calories. 8. An airplane is flying 55 miles per hour Northwest. 9. A violent wind gust was measured 35 knots. 10. An astronaut with a mass of 50-kilogram weights 185.55 Newton on the surface of planet Mars. PRACTICE EXERCISE 4 “Vectors for Victor” Directions: Solve the following problems. Provide a sheet of paper for your answers, solutions and drawing. 1. Use the graphical method to determine the resultant vector of the following:  A = 300 m East B = 215 m North C = 480 m, 35̊ West of North 2. A mountain climbing expedition establishes a base camp and two intermediate camps, A and B. Camp A is 11,200 m east of and 3,200 m above base camp. Camp B is 8400 m east of and 1700 m higher than Camp A. Determine the displacement between base camp and Camp B. Instruction: Please write your learning from the above discussion. Write your learning in your notebook/answer sheet. Upon reading the lesson above, I learned that ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ and realized that ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ WRITTEN WORKS MULTIPLE CHOICES: Choose the letter of the correct answer and write it on your provided answer sheet. _____1. Which of the following do not show a unit of measure frequently used in daily life? A. Filling unleaded gasoline in your motorcycle. B. A nurse carefully measuring the quantity of medicine to be given to the patient.  C. Working out the amount of paint required in painting your home. D. Measuring the intensity of light bulb at home. _____2. What Unit of measurement is appropriate to measure the distance between two cities? A. centimeter B. meter C. kilometer D. feet _____3. The average beat of human heart is 80 beats per minute. How many beats is this in one hour? Express your answer in scientific notation. A. 4.8 x 10-3 beats/min B. 4.8 x 103 beats/min C. 48 x 102 beats/min D. 48.0 x 103 beats/min _____4. In the figure 80.004, how many significant digits is present? A. 2 B. 3 C. 4 D. 5 _____5. A high fever can be presenting symptoms for covid-19. After effectively checking your body temperature you found out that it measures 38.6°. If 1° is equal to 273.15 kelvins, what is your equivalent temperature in kelvin? A. 1 543.59 kelvins B. 1953.48 kelvins C. 10 590.43 kelvins D. 10 543.59 kelvins _____6. What symbol is typically used to draw a vector? A. Arrow B. Box C. Hashtag D. The letter X _____7. Which of the following measurement is a vector quantity? A. Mass B. Speed C. Time D. Velocity _____8. Determine which is a scalar quantity on the following situations. A. A car is speeding eastward. B. The wind is blowing from the south. C. The temperature outside is 38o C. D. The water is flowing due north at 5 km/hr.  _____9. A motorboat heads due east at 5.0 m/s across a river that flows toward the south at a speed of 5.0 m/s. What is the resultant velocity relative to an observer on the shore? A. 3.2 m/s to the southeast B. 5.0 m/s to the southeast C. 7.1 m/s to the southeast D. 10.0 m/s to the southeast _____10. An airplane heads due north at 100 m/s through a 30 m/s cross wind blowing from the east to the west. Determine the resultant velocity of the airplane (relative to due north). A. 72 m/s, 15° west of north B. 89 m/s, 16° west of north C. 97 m/s, 16° west of north D. 104 m/s, 17° west of north PERFORMANCE TASK Directions: Answer the following. Provide a sheet of paper for your answers, solutions and drawing. 1. A motorcycle is driven 50 km west, then 30 km south, and 25 km, 30o west of south. Find the total displacement of the motorcycle using the component method? 2. As a commuter? Have you tried any mobile app to help you cope with your daily navigation problems? Why do you use such an app? What other applications of vectors do you know that are useful in different industries?  Rosario Laurel-Sotto. Physics Textbook. Science in today’s World Series, Pages 22-32.  Paul G. Hewitt. Conceptual Physics. Third Edition Pages 28-31.  Vector Addition and Subtraction: Analytical Methods. https://courses.lumenlearning.com/physics/chapter/test-vector-addition-and-subtraction- analytical-methods/  Vector Addition and Subtraction: Graphical Methods. https://courses.lumenlearning.com/physics/chapter/3-2-vector-addition-and-subtraction- graphical-methods/  Vectors - Motion and Forces in Two Dimensions - Lesson 1 - Vectors: Fundamentals and Operations. https://www.physicsclassroom.com/class/vectors/Lesson-1/Component- Addition  https://www.vectorstock.com/royalty-free-vector/x-and-y-axis-vector-7810341  https://www.twinkl.fr/illustration/compass-map-icon  The Physics Hypertexbook.vector-addition practice https://physics.info/vector-addition/practice.shtml  http://hyperphysics.phy-astr.gsu.edu/hbase/mass.html  https://www.sixt.com/magazine/tips/top-traffic-apps/  Car vector created by freepik - https://www.freepik.com/vectors/car  School vector created by pch.vector - www.freepik.com/vectors/school  Love vector created by catalyststuff - www.freepik.com/vectors/love  Background vector created by macrovector - www.freepik.com/vectors/background  Background vector created by macrovector_official - www.freepik.com/vectors/background  School vector created by macrovector - https://www.freepik.com/vectors/school Key to Practice Exercises Lesson 1 Practice Exercise 1 1. Feet 2. Hours 3. Milligram 4. Minutes 5. Centimeter 6. Kilogram 7. Gram 8. Hours 9. Ton 10. Hours Practice Exercise 2 39.4 𝑖𝑛𝑐ℎ𝑒𝑠 1.) 5 meters = 1 𝑚𝑒𝑡𝑒𝑟 = 197 inches 1 000 𝑔𝑟𝑎𝑚 1 000 𝑚𝑖𝑙𝑙𝑖𝑔𝑟𝑎𝑚 2.) 8 000 000 kilogram = 1 𝑘𝑖𝑙𝑜𝑔𝑟𝑎𝑚 x 1 𝑔𝑟𝑎𝑚 = 8 000 000 000 000 8 x 1012 milligrams Practice Exercise 3 A. 1. 1 2. 3 3. 6 4. 5 5. 4 B. 1. 0.0823  2. 9.34 x 1011 3. 6 100 000 4. 0. 000215 5. 6 x 103 Lesson 2 Practice Exercise 1 Z T A D D S D E N S I T Y O D Q I A R E M A S S G E N E R T I A H G D I S P L A C E M E N T S C S D R A G A C T I V I T Y O T C P S M A N N E Y G R E N E W A E E C O E V E T E R M A L L E N L E A B I O I M P cU L S E D I C E D L L E C O T R A G R A N G E R O A E O R E O Y E N O H U H I A N R L E O M O M E N T U M T D T c E E A K A I Q F E U N R E T R I V E C T O R S R C U E N A E C O I S A R E A W E R W O R K E E N M S B Z Y W I N O F F L A N E I E R U S S E R P F V O L U M E S Practice Exercise 2 1. Dela Cruz 6. Dela Cruz 2. Dela Cruz 7. Juan 3. Juan 8. Dela Cruz 4. Juan 9. Dela Cruz 5. Juan 10. Dela Cruz 11. Practice Exercise 3 SCALE: 1cm = 100m 1. A=300m E B=215m N C=480m,35 W of N R=522m, 68̊ Northwest 2. Add vectors in the same direction with "ordinary" addition. x = 11,200 m + 8,400 m x = 19,600 m y = 3200 m + 1700 m y = 4900 m Add vectors at right angles with a combination of Pythagorean theorem for magnitude… r = √(x2 + y2) r = √[(19,600 m)2 + (4,900 m)2] r = 20,200 m and tangent for direction. y 4,900m tan    x 19,600m   14.0 Camp B is 20,200 m away from base camp at an angle of elevation of 14.0°.