Q: A projectile is launched with initial velocity $$v_i at $$angle $$\theta. $$What is the formula for its horizontal range $$R ($$assuming it lands at the same height it was launched)?

$$R = \frac{v_i^2$ \sin 2\theta}{g}$$

Q: A projectile is launched from ground level with initial speed $$v_i at $$angle $$\theta. $$What is the maximum height $$H it $$reaches?

$$H = \frac{v_i^2$ \sin^2$\theta}{2g}$$

Question 1

A ball is thrown horizontally from the top of a cliff. Neglecting air resistance, which of the following statements about its motion is correct?

Accepted Answer

The ball's horizontal velocity remains constant, while its vertical velocity increases in magnitude due to gravity.

Question 2

A projectile is launched with an initial velocity $$\vec{v}_i at an $$angle $$	heta$$ above the horizontal. What is the vertical component of its initial velocity?

Accepted Answer

$$v_{i,y} = v_i \sin	heta$$

Question 3

Which equation correctly describes the vertical displacement $$\Delta y of a $$projectile under constant acceleration due to gravity?

Accepted Answer

$$\Delta y = v_{i,y} \Delta t + \frac{1}{2} a_y \Delta t^2$

Question 4

A ball is dropped from rest and another is shot horizontally from the same height at the same time. Neglecting air resistance, which hits the ground first?

Accepted Answer

Both hit the ground at the same time.

Question 5

A cart moves with constant velocity $$v$$ and a ball is thrown vertically upward from it. Where does the ball land relative to the cart?

Accepted Answer

Directly above the cart.

Question 6

In projectile motion, what is the value of the horizontal acceleration $$a_x$$?

Accepted Answer

$$a_x = 0$$

Question 7

A projectile is launched at an angle $$	heta$$ with initial speed $$v_i. $$What is the formula for its instantaneous speed $$v at $$any time $$t$$?

Accepted Answer

$$v = \sqrt{v_{x}^2 + v_{y}^2}$$

Question 8

A cannon simultaneously fires two shells at ships A and B, following different parabolic trajectories. What determines which shell has a longer time of flight?

Accepted Answer

The shell with the higher initial vertical velocity component.

Question 9

If gravity were suddenly turned off, what would happen to the trajectory of a projectile?

Accepted Answer

It would continue in a straight line tangent to its path at the point gravity was turned off.

Question 10

Which of the following best describes the acceleration vector of a projectile in flight (neglecting air resistance)?

Accepted Answer

It points downward and has magnitude $$g.$$

Question 11

A projectile is launched with initial velocity $$v_i at $$angle $$	heta. $$What is the formula for its horizontal range $$R ($$assuming it lands at the same height it was launched)?

Accepted Answer

$$R = \frac{v_i^2$ \sin 2	heta}{g}$$

Question 12

Which of the following is true about the velocity vector of a projectile at the peak of its trajectory?

Accepted Answer

It is entirely horizontal.

Question 13

A ball is thrown at an angle $$	heta$$ above the horizontal. Which component of its velocity changes during flight?

Accepted Answer

Only the vertical component.

Question 14

Given the equations for displacement in 2D motion, which correctly expresses the $$x-$$component of displacement?

Accepted Answer

$$\Delta x = v_{i,x} \Delta t$$

Question 15

A projectile is launched from ground level with initial speed $$v_i at $$angle $$	heta. $$What is the maximum height $$H it $$reaches?

Accepted Answer

$$H = \frac{v_i^2$ \sin^2$	heta}{2g}$$

Question 16

Which of the following is a correct statement about the independence of horizontal and vertical motions in projectile motion?

Accepted Answer

The horizontal and vertical motions are independent except for sharing the same time of flight.

Question 17

A projectile is launched at $$30^\circ$$ above the horizontal with initial speed $$20\,\mathrm{m/s}. $$What is its initial vertical velocity component?

Accepted Answer

$$v_{i,y} = 20 \sin 30^\circ = 10\,\mathrm{m/s}$$

Question 18

Which of the following best explains why a ball thrown upward from a moving cart lands back on the cart?

Accepted Answer

The ball retains the horizontal velocity of the cart throughout its flight.

Question 19

A projectile is launched with initial velocity $$v_i at $$angle $$	heta. $$What is the time of flight $$T if it $$lands at the same height it was launched?

Accepted Answer

$$T = \frac{2 v_i \sin	heta}{g}$$

2D Motion and Projectile Motion: Study Notes for College Physics

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