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Questions and Answers
What is the correct mass of a sugar grain that weighs 5 milligrams in grams?
What is the correct mass of a sugar grain that weighs 5 milligrams in grams?
- 5 × 10⁻² grams
- 5 × 10² grams
- 5 × 10¹ grams
- 5 × 10⁻³ grams (correct)
When does projectile motion start?
When does projectile motion start?
- After the peak
- At the peak
- At the end of the motion
- Before the peak (correct)
What type of motion is indicated when an object is thrown upwards and then falls back down?
What type of motion is indicated when an object is thrown upwards and then falls back down?
- Projectile motion (correct)
- Circular motion
- Linear motion
- Free-fall motion
What happens to the horizontal acceleration of a projectile during its motion?
What happens to the horizontal acceleration of a projectile during its motion?
What is the area of a park measuring 12.3 km² in m²?
What is the area of a park measuring 12.3 km² in m²?
What occurs to the vertical acceleration of a projectile during its motion?
What occurs to the vertical acceleration of a projectile during its motion?
What is the horizontal component of the velocity for an object launched with an initial velocity of 20 m/s at an angle of 30 degrees?
What is the horizontal component of the velocity for an object launched with an initial velocity of 20 m/s at an angle of 30 degrees?
What is the vertical velocity component of a projectile after 3 seconds, launched with an initial velocity of 20 m/s at an angle of 30 degrees?
What is the vertical velocity component of a projectile after 3 seconds, launched with an initial velocity of 20 m/s at an angle of 30 degrees?
What is the final vertical velocity of the projectile after 4 seconds?
What is the final vertical velocity of the projectile after 4 seconds?
Which expression can be used to find the angle θ if given the opposite side length of 6 and the adjacent side length of 10?
Which expression can be used to find the angle θ if given the opposite side length of 6 and the adjacent side length of 10?
Which of the following options represents a vector quantity?
Which of the following options represents a vector quantity?
What is the direction of the hiker's total displacement vector with respect to due south after walking 2.00 km south and then east?
What is the direction of the hiker's total displacement vector with respect to due south after walking 2.00 km south and then east?
How long does it take for a projectile launched at an initial velocity of 40 m/s at a 30-degree angle to reach maximum height?
How long does it take for a projectile launched at an initial velocity of 40 m/s at a 30-degree angle to reach maximum height?
How far does a motorcycle travel in 10 seconds if it accelerates at a rate of 3.0 m/s² from rest?
How far does a motorcycle travel in 10 seconds if it accelerates at a rate of 3.0 m/s² from rest?
What is the vertical component of the initial velocity for a projectile launched at 40 m/s at an angle of 30 degrees?
What is the vertical component of the initial velocity for a projectile launched at 40 m/s at an angle of 30 degrees?
If a hiker travels 2.00 km due south before walking due east, what is the total distance traveled regardless of direction?
If a hiker travels 2.00 km due south before walking due east, what is the total distance traveled regardless of direction?
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Study Notes
Units and Conversions
- The mass of a sugar grain is 5 milligrams, which equals 5 × 10⁻³ grams.
- Area conversion example: A park with an area of 12.3 km² equals 1.23 × 10⁶ m².
Types of Motion
- Full-projectile motion begins before the peak of the trajectory and consists of various motion types.
- Sarah observes projectile motion as an object is thrown upwards and then falls back due to gravity.
- Horizontal acceleration of a projectile remains constant throughout its motion.
- Vertical acceleration of a projectile remains constant at approximately -9.8 m/s² due to gravity.
Velocity Components
- The horizontal component of an object's velocity launched at 20 m/s and 30 degrees is approximately 17.32 m/s.
- The vertical velocity component after 3 seconds of an object launched with 20 m/s at 30 degrees is -19.4 m/s.
Projectile Challenges
- An object projected vertically with an initial velocity of 9 m/s reaches a final vertical velocity of -30.2 m/s after 4 seconds.
Trigonometry in Motion
- To calculate angle θ in a triangle, use the expression θ = cos⁻¹(6/10) or θ = tan⁻¹(10/6) depending on the known sides.
Vector and Scalar Quantities
- Vector quantities include forces (e.g., wind force), while scalar quantities include volume, speed, and population.
Displacement Calculations
- A hiker’s total displacement after walking 2.00 km south then east is 2.40 km with a direction of 34° east of south, calculated using cosine law.
Time to Maximum Height
- A projectile launched with an initial velocity of 40 m/s at 30 degrees takes 2 seconds to reach maximum height.
Distance and Acceleration
- A motorcycle accelerating from rest at 3.0 m/s² will travel 150 meters in 10 seconds, calculated using the formula d = ½ at².
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