ch 3 physics

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Questions and Answers

What is the correct formula to calculate the horizontal displacement of a projectile?

x = v_y * t

x = v_x * t (correct)

x = v_i * t

x = v * sin(θ) * t

If a projectile is launched horizontally off a 22.0-meter high hill, how can its time of flight be determined?

Using the equation t = h/g

By using the horizontal velocity and calculating distance

Using the equation t = √(2h/g) (correct)

By directly measuring the horizontal distance covered

In projectile motion, what does the component v_x represent?

The total velocity of the projectile

The vertical velocity component

The horizontal velocity component (correct)

The time of flight of the projectile

When considering projectile motion, how is the vertical component of velocity (v_y) calculated?

v_y = v * sin(θ) Signup and view all the answers

If a projectile is launched at an angle of 30 degrees with an initial velocity of 10 m/s, what can be said about its horizontal motion?

The horizontal velocity component is determined by v_x = v * cos(30°) Signup and view all the answers

What must be done before adding two or more vectors together?

Convert them to Cartesian coordinates Signup and view all the answers

Which formula represents the x-component of a vector A?

$A_x = A ext{cos} heta$ Signup and view all the answers

Which analytical method is more concise and accurate for vector operations?

Analytical methods using trigonometry Signup and view all the answers

In projectile motion, what is the behavior of the x and y components of the motion?

They are independent and analyzed separately Signup and view all the answers

What is used to find the magnitude of the resultant vector from its components?

The Pythagorean theorem Signup and view all the answers

If an object is projected horizontally, which of the following statements is true about its motion?

The horizontal component of velocity remains constant Signup and view all the answers

What is the effect of gravitational force on the motion of a projectile?

It only affects the vertical motion Signup and view all the answers

Which equation would you use to find the direction of a vector R when given its components?

$ heta = ext{tan}^{-1}rac{A_y}{A_x}$ Signup and view all the answers

What is the graphical method called that is used for vector addition?

Head-to-Tail Method Signup and view all the answers

If a vector A has a magnitude of 10 km north and vector B has a magnitude of 5 km west, what is the resultant vector A + B?

12.5 km at 63.43 degrees Signup and view all the answers

When subtracting vector B from vector A graphically, what does 'A - B' represent?

Vector A added to the negative of vector B Signup and view all the answers

If vector A has a magnitude of 6 and points north, and vector B has a magnitude of 8 and points east, what is the magnitude of B - A?

10 km Signup and view all the answers

What happens to the magnitude and direction of a vector when it is multiplied by a negative scalar?

Magnitude remains the same, direction reverses Signup and view all the answers

What is required to determine the direction of the resultant vector in vector addition?

The angle it makes with the reference frame Signup and view all the answers

How is the negative of vector B represented graphically?

It is the same length but points in the opposite direction Signup and view all the answers

What does vector addition being commutative imply?

The order of adding vectors does not affect the resultant Signup and view all the answers

Study Notes

Two Dimensional Kinematics

Two-dimensional kinematics describes motion along a curved path on a flat surface, like a ball on a pool table or a skater on an ice rink.
A vector quantity is fully described by magnitude and direction (e.g., velocity).
A scalar quantity is fully described by magnitude alone (e.g., speed).

Vector Addition and Subtraction - Graphical Method

The head-to-tail method: The tail of the second vector is placed at the head of the first vector. The resultant vector starts at the tail of the first vector and ends at the head of the second vector.
Vector addition is commutative: A + B = B + A.

Vector Addition and Subtraction - Analytical Method

Analytical methods use geometry and trigonometry to find the resultant vector.
Cartesian components: These are the projections of a vector onto the x and y axes.
To find the components, use trigonometry: Ax = A cos θ and Ay = A sin θ.
Once the components are found, add the x-components and the y-components separately to obtain the resultant vector.

Projectile Motion

Projectile motion is the motion of an object thrown or projected into the air, affected only by gravity.
The path of a projectile is called the trajectory.
Horizontal and vertical motions are independent.
The horizontal motion has constant velocity (ax = 0).
The vertical motion has constant acceleration (ay = -g).

Projectile Motion Analysis Steps

Resolve the motion into horizontal (x) and vertical (y) components.
Treat horizontal and vertical motions separately.
Solve for the unknowns (typically time) using appropriate kinematic equations in each direction.
Combine the horizontal and vertical components to find the overall displacement and velocity.

Horizontally Launched Projectiles

The horizontal displacement of a horizontally launched projectile is given by x = vix * t.

Examples of Projectile Problems

Various projectile motion examples are given (varying launch heights, angles, and initial velocities).

Determining Components of a Velocity Vector

The horizontal component of velocity is vx = v cos θ
The vertical component of velocity is vy = v sin θ

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Description

Explore the principles of two-dimensional kinematics, including vector addition and subtraction using both graphical and analytical methods. Understand how to describe motion with vector and scalar quantities, and learn to compute resultant vectors using geometry and trigonometry.