Q: A ball is thrown horizontally from the top of a 45 m high building with an initial speed of 8 m/s. Neglecting air resistance, how long does it take for the ball to hit the ground?

$$t = \sqrt{\frac{2 \times 45}{9.8}}$$

Q: A boulder rolls off a 33.0 m high cliff and lands 15 m away from the base. What was its horizontal velocity as it left the cliff?

$$v_{ix} = \frac{15}{\sqrt{\frac{2 \times 33.0}{9.8}}}$$

Q: A pelican flying horizontally at 7.6 m/s drops a fish from a height of 2.7 m. How far does the fish travel horizontally before hitting the water?

$$\Delta x = 7.6 \times \sqrt{\frac{2 \times 2.7}{9.8}}$$

Q: If a projectile is launched at an angle $$\theta$$ with initial speed $$v_0$$, what is the formula for its maximum height?

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: Which equation correctly gives the range $$R of a $$projectile launched from ground level at speed $$v_0$$ and angle $$\theta ($$neglecting air resistance)?

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

Question 1

A ball is thrown horizontally from the top of a 45 m high building with an initial speed of 8 m/s. Neglecting air resistance, how long does it take for the ball to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2 	imes 45}{9.8}}$$

Question 2

Which statement best describes the horizontal component of velocity for a projectile (neglecting air resistance)?

Accepted Answer

It remains constant throughout the motion.

Question 3

A soccer ball is kicked at an initial speed of 20 m/s at an angle of $$30^\circ$$ above the horizontal. What is the initial vertical component of velocity?

Accepted Answer

$$v_{iy} = 20 \sin 30^\circ$$

Question 4

A boulder rolls off a 33.0 m high cliff and lands 15 m away from the base. What was its horizontal velocity as it left the cliff?

Accepted Answer

$$v_{ix} = \frac{15}{\sqrt{\frac{2 	imes 33.0}{9.8}}}$$

Question 5

Which of the following 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 6

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

Accepted Answer

$$\Delta x = 7.6 	imes \sqrt{\frac{2 	imes 2.7}{9.8}}$$

Question 7

If a projectile is launched at an angle $$	heta$$ with initial speed $$v_0$$, what is the formula for its maximum height?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 8

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

Accepted Answer

In the cart

Question 9

Which equation correctly gives the range $$R of a $$projectile launched from ground level at speed $$v_0$$ and angle $$	heta ($$neglecting air resistance)?

Accepted Answer

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

Question 10

A penny is dropped from rest while another is launched horizontally from the same height. Neglecting air resistance, which penny reaches the ground first?

Accepted Answer

Both at the same time

Question 11

Which formula gives the vertical displacement $$\Delta y$$ for a projectile with initial vertical velocity $$v_{iy}$$ after time $$t$$?

Accepted Answer

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

Question 12

A projectile is launched at $$25^\circ$$ above the horizontal with a speed of 18 m/s. What is the initial horizontal velocity?

Accepted Answer

$$v_{ix} = 18 \cos 25^\circ$$

Question 13

Which of the following best explains why the vertical position of two balls (one dropped, one launched horizontally) is identical at identical times?

Accepted Answer

Both experience the same vertical acceleration due to gravity.

Question 14

Which graph best represents the vertical velocity $$v_y of a $$projectile as a function of time?

Accepted Answer

A straight line with negative slope

Question 15

A projectile is launched from ground level at $$v_0$$ and angle $$	heta. $$What is the time of flight until it returns to ground level?

Accepted Answer

$$t = \frac{2 v_0$ \sin 	heta}{g}$$

Question 16

Which equation gives the final vertical velocity $$v_{fy}$$ for a projectile after time $$t$$?

Accepted Answer

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

Question 17

A projectile is launched at $$v_0$$ and angle $$	heta. $$What is the formula for its initial velocity vector?

Accepted Answer

$$\vec{v}_0 = v_0$ \cos 	heta \hat{i} + v_0$ \sin 	heta \hat{j}$$

Question 18

Which of the following is NOT a correct assumption for ideal projectile motion?

Accepted Answer

Air resistance is significant

Question 19

A soccer player kicks a ball at 15 m/s, $$25^\circ NE $$down the field. What is the formula for the ball's total air time?

Accepted Answer

$$t = \frac{2 	imes 15 \sin 25^\circ}{9.8}$$

2D Projectile Motion: Concepts, Equations, and Applications

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