Q: A projectile is launched from the edge of a cliff with an initial velocity of $$v_0 = 30$$\ \mathrm{m/s}$$ at an angle of 60$$^\circ$$ above the horizontal. The cliff is 81$$\ \mathrm{m}$$ above the ground. What is the initial vertical component of the velocity v$$_{0y}$$?

$$v_{0y} = 30 \times \sin 60^\circ = 25.98\ \mathrm{m/s}$$

Q: Given the same scenario, what is the initial horizontal component of the velocity $$v_{0x}$$?

$$v_{0x} = 30 \times \cos 60^\circ = 15\ \mathrm{m/s}$$

Question 1

A projectile is launched from the edge of a cliff with an initial velocity of $$v_0 = 30$$\ \mathrm{m/s}$$ at an angle of 60$$^\circ$$ above the horizontal. The cliff is 81$$\ \mathrm{m}$$ above the ground. What is the initial vertical component of the velocity v$$_{0y}$$?

Accepted Answer

$$v_{0y} = 30 	imes \sin 60^\circ = 25.98\ \mathrm{m/s}$$

Question 2

Given the same scenario, what is the initial horizontal component of the velocity $$v_{0x}$$?

Accepted Answer

$$v_{0x} = 30 	imes \cos 60^\circ = 15\ \mathrm{m/s}$$

Question 3

How long does it take for the projectile to reach the ground from the cliff?

Accepted Answer

$$t = \frac{-v_{0y} + \sqrt{v_{0y}^2 + 2g h}}{g}$$

Question 4

What is the vertical velocity $$v_{fy} of $$the projectile just before it hits the ground?

Accepted Answer

$$v_{fy} = -\sqrt{v_{0y}^2 + 2g h}$$

Question 5

What is the magnitude of the final velocity $$v_f$$ just before the projectile hits the ground?

Accepted Answer

$$v_f = \sqrt{v_{fx}^2 + v_{fy}^2}$$

Question 6

If $$v_{fx} = 15\ \mathrm{m/s}$$ and $$v_{fy} = -47.57\ \mathrm{m/s}$$, what is the magnitude of the final velocity?

Accepted Answer

$$v_f = \sqrt{15^2$ + 47.57^2$} = 49.91\ \mathrm{m/s}$$

Question 7

What is the horizontal distance $$x_f$$ from the base of the cliff to the point where the projectile lands?

Accepted Answer

$$x_f = v_{0x} \cdot t$$

Question 8

Which of the following best describes the acceleration of the projectile during its flight (neglecting air resistance)?

Accepted Answer

The acceleration is constant and equal to $$g$$ downward.

Question 9

At the highest point of the projectile's trajectory, which statement is true?

Accepted Answer

The vertical component of velocity is zero.

Question 10

If the angle of projection is increased while keeping the initial speed the same, what happens to the range (horizontal distance) of the projectile (from the same height)?

Accepted Answer

The range first increases, reaches a maximum, then decreases.

Question 11

If the projectile is launched from the ground (not from a cliff) with the same initial speed and angle, what would be the time of flight?

Accepted Answer

$$t = \frac{2 v_{0y}}{g}$$

Question 12

Which equation would you use to find the vertical position $$y of $$the projectile at any time $$t$$?

Accepted Answer

$$y = y_0$ + v_{0y} t - \frac{1}{2} g t^2$

Question 13

A student claims that the horizontal velocity of the projectile changes during flight. Is this correct?

Accepted Answer

No, the horizontal velocity remains constant if air resistance is neglected.

Question 14

What is the direction of the final velocity vector just before the projectile hits the ground?

Accepted Answer

$$	heta = \arctan\left(\frac{|v_{fy}|}{v_{fx}}ight)$$ below the horizontal

Projectile Motion: Analysis and Calculations

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