Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following expressions gives the horizontal range $$R ($$assuming it lands at the same height)?

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

Q: A projectile is launched with initial velocity $$v_0 at $$angle $$\theta. $$What is the time of flight if it lands at the same height?

$$t = \dfrac{2 v_0$ \sin \theta}{g}$$

Q: A projectile is launched at $$v_0$$ and $$\theta. $$What is the vertical component of velocity at time $$t$$?

$$v_y = v_0$ \sin \theta - g t$$

Q: A projectile is launched at $$v_0$$ and $$\theta. $$What is the maximum height reached?

$$h_{max} = \dfrac{v_0$^2 \sin^2$ \theta}{2g}$$

Question 1

A mountain climber jumps horizontally across a crevasse that is $$h = 2.74\ \mathrm{m}$$ lower and $$w = 4.10\ \mathrm{m}$$ away. What is the minimum initial speed $$v_0$$ required for the climber to safely reach the other side?

Accepted Answer

$$v_0$$ = \dfrac{w}{\sqrt{2h/g}}$$

Question 2

For the same mountain climber, what is the time $$t it $$takes to reach the other side?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 3

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following expressions gives the horizontal range $$R ($$assuming it lands at the same height)?

Accepted Answer

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

Question 4

A football is kicked at an angle of $$44.0^\circ$$ above the horizontal and lands $$37.0\ \mathrm{m}$$ away at the same level. What was the initial speed $$v_0 of $$the ball?

Accepted Answer

$$v_0 = 19.1$$\ \mathrm{m/s}$$

Question 5

A projectile is launched at $$	heta = 30^\circ$$ and another at $$	heta = 60^\circ$$ with the same initial speed. Which statement is true about their ranges?

Accepted Answer

Both projectiles have the same range.

Question 6

A golfer hits a ball with $$v_0 = 15.0$$\ \mathrm{m/s}$$ at 62.0$$^\circ$$ above the horizontal. If the ball lands 2.58$$\ \mathrm{s}$$ later, what is the vertical height y$ of the green above the starting point?

Accepted Answer

$$y = 1.51\ \mathrm{m}$$

Question 7

At what angle should a projectile be launched to achieve maximum range on level ground?

Accepted Answer

$$45^\circ$$

Question 8

A projectile is launched horizontally from a height $$h$$ with speed $$v_0. $$What is the vertical component of its velocity just before it lands?

Accepted Answer

$$v_y = -\sqrt{2gh}$$

Question 9

A projectile is launched with initial velocity $$v_0 at $$angle $$	heta. $$What is the time of flight if it lands at the same height?

Accepted Answer

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

Question 10

A climber jumps horizontally with $$v_0 = 5.49$$\ \mathrm{m/s}$$ from a height of 2.74$$\ \mathrm{m}$$. What is the magnitude of the velocity just before landing?

Accepted Answer

$$v = \sqrt{(5.49)^2$ + (7.33)^2$}\ \mathrm{m/s}$$

Question 11

Why is the negative solution for $$v_y$$ chosen as the physically correct result when the climber is $$1.00\ \mathrm{m}$$ above the lower ice level?

Accepted Answer

Because the climber is moving downward at that point.

Question 12

A projectile is launched at $$v_0$$ and $$	heta. $$What is the vertical component of velocity at time $$t$$?

Accepted Answer

$$v_y = v_0$ \sin 	heta - g t$$

Question 13

A projectile is launched at $$v_0 = 15.0$$\ \mathrm{m/s}$$, $$	heta = 62.0^\circ$$. What is the horizontal distance traveled after 2.58$$\ \mathrm{s}$$?

Accepted Answer

$$x = 18.2\ \mathrm{m}$$

Question 14

Which of the following best describes the trajectory of a projectile (neglecting air resistance)?

Accepted Answer

A parabola

Question 15

A projectile is launched at $$v_0$$ and $$	heta. $$What is the maximum height reached?

Accepted Answer

$$h_{max} = \dfrac{v_0$^2 \sin^2$ 	heta}{2g}$$

Two-Dimensional Kinematics: Projectile Motion and Applications

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