Q: A boulder rolls off a $$33.0\ \mathrm{m}$$ high cliff and lands $$15.0\ \mathrm{m}$$ away from the base. How long does it take to hit the ground? (Neglect air resistance)

$$t = \sqrt{\frac{2 \times 33.0}{9.8}}$$

Q: A projectile is launched horizontally from a $$20\ \mathrm{m}$$ high cliff. How long does it take to reach the ground?

$$t = \sqrt{\frac{2 \times 20}{9.8}}$$

Q: If a projectile is launched at an angle $$\theta$$ with initial speed $$v_0$$, which formula gives the range (horizontal distance) on level ground?

$$R = \frac{v_0$^2 \sin(2\theta)}{g}$$

Question 1

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

Accepted Answer

Both at the same time

Question 2

Which of the following best describes the acceleration of a projectile in 2D motion (neglecting air resistance)?

Accepted Answer

Constant acceleration downward and zero acceleration horizontally

Question 3

A soccer ball is kicked at an initial speed of $$12\ \mathrm{m/s} at an $$angle of $$25^\circ$$ above the horizontal. What is the initial vertical component of its velocity?

Accepted Answer

$$12 \sin(25^\circ)$$

Question 4

Which equation correctly gives the horizontal displacement $$\Delta x$$ for a projectile launched horizontally from a cliff?

Accepted Answer

$$\Delta x = v_{ix} t$$

Question 5

A boulder rolls off a $$33.0\ \mathrm{m}$$ high cliff and lands $$15.0\ \mathrm{m}$$ away from the base. How long does it take to hit the ground? (Neglect air resistance)

Accepted Answer

$$t = \sqrt{\frac{2 	imes 33.0}{9.8}}$$

Question 6

A pelican flying horizontally at $$7.6\ \mathrm{m/s}$$ drops a fish from a height of $$2.7\ \mathrm{m}. $$How far does the fish travel horizontally before hitting the water?

Accepted Answer

$$d = v_{ix} \sqrt{\frac{2h}{g}}$$

Question 7

Which statement is true about the independence of the x and y components in projectile motion?

Accepted Answer

The x and y components are independent and can be analyzed separately

Question 8

A cart rolls across a flat surface at constant velocity and launches a ball straight up. Where does the ball land relative to the cart?

Accepted Answer

In the cart

Question 9

Which of the following equations gives the vertical displacement $$\Delta y$$ for a projectile with initial vertical velocity $$v_{iy}$$ and constant acceleration $$a_y$$?

Accepted Answer

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

Question 10

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for its initial horizontal velocity component?

Accepted Answer

$$v_0$$ \cos 	heta$$

Question 11

Which graph best represents the velocity in the horizontal direction for a projectile (neglecting air resistance)?

Accepted Answer

A horizontal line (constant velocity)

Question 12

For a projectile launched horizontally from a cliff, what is the initial vertical velocity $$v_{iy}$$?

Accepted Answer

$$0$$

Question 13

Which equation can be used to find the final vertical velocity $$v_{fy} of a $$projectile after time $$t$$?

Accepted Answer

$$v_{fy} = v_{iy} + a_y t$$

Question 14

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

Accepted Answer

$$20 \sin(30^\circ)$$

Question 15

Which of the following is true about the acceleration in the horizontal direction for projectile motion (neglecting air resistance)?

Accepted Answer

It is zero

Question 16

A projectile is launched at an angle. At the peak of its trajectory, what is its vertical velocity?

Accepted Answer

Zero

Question 17

Which equation relates the final vertical velocity squared to the initial vertical velocity squared, acceleration, and vertical displacement?

Accepted Answer

$$v_{fy}^2 = v_{iy}^2 + 2 a_y \Delta y$$

Question 18

A projectile is launched horizontally from a $$20\ \mathrm{m}$$ high cliff. How long does it take to reach the ground?

Accepted Answer

$$t = \sqrt{\frac{2 	imes 20}{9.8}}$$

Question 19

If a projectile is launched at an angle $$	heta$$ with initial speed $$v_0$$, which formula gives the range (horizontal distance) on level ground?

Accepted Answer

$$R = \frac{v_0$^2 \sin(2	heta)}{g}$$

2D Projectile Motion: Principles and Problem Solving

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