Q: A ball is launched from the ground at an angle of $$35.0^\circ$$ above the horizontal with an initial speed of $$20.0\ \mathrm{m/s}. $$What is the initial vertical component of its velocity?

$$v_{0y} = 20.0\ \mathrm{m/s} \times \sin 35.0^\circ = 11.5\ \mathrm{m/s}$$

Q: A helicopter is flying horizontally at $$11\ \mathrm{m/s}$$ and begins to accelerate upward at $$0.96\ \mathrm{m/s^2$}. $$What is the vertical displacement after $$5.3\ \mathrm{s}$$?

$$y = 0 + 0 \times 5.3 + \frac{1}{2} \times 0.96 \times (5.3)^2$ = 13\ \mathrm{m}$$

Q: A projectile is launched from the origin with $$v_0 = 20.0$$\ \mathrm{m/s}$$ at 35.0$$^\circ$$ above the horizontal. What is the x$-position after 1.00$$\ \mathrm{s}$$?

$$x = 0 + 20.0 \cos 35.0^\circ \times 1.00 = 16.4\ \mathrm{m}$$

Q: A helicopter moves horizontally at $$11\ \mathrm{m/s}$$ and accelerates upward at $$0.96\ \mathrm{m/s^2$}. $$What is the $$y-$$component of its velocity after $$5.3\ \mathrm{s}$$?

$$v_y = 0 + 0.96 \times 5.3 = 5.1\ \mathrm{m/s}$$

Q: A projectile is launched from the ground with $$v_0 = 20.0$$\ \mathrm{m/s}$$ at 35.0$$^\circ$$. What is the maximum height it reaches?

$$y = \frac{(v_{0y})^2$}{2g} = \frac{(11.5)^2$}{2 \times 9.81} = 6.74\ \mathrm{m}$$

Q: A ball is thrown horizontally from a height of $$10\ \mathrm{m}$$ with a speed of $$5\ \mathrm{m/s}. $$How far from the base of the cliff does it land? (Neglect air resistance, $$g = 9.81\ \mathrm{m/s^2$})$$

First, $$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 10}{9.81}} = 1.43\ \mathrm{s}$$; then $$x = v_{0x} t = 5 \times 1.43 = 7.15\ \mathrm{m}$$

Question 1

A ball is launched from the ground at an angle of $$35.0^\circ$$ above the horizontal with an initial speed of $$20.0\ \mathrm{m/s}. $$What is the initial vertical component of its velocity?

Accepted Answer

$$v_{0y} = 20.0\ \mathrm{m/s} 	imes \sin 35.0^\circ = 11.5\ \mathrm{m/s}$$

Question 2

A helicopter is flying horizontally at $$11\ \mathrm{m/s}$$ and begins to accelerate upward at $$0.96\ \mathrm{m/s^2$}. $$What is the vertical displacement after $$5.3\ \mathrm{s}$$?

Accepted Answer

$$y = 0 + 0 	imes 5.3 + \frac{1}{2} 	imes 0.96 	imes (5.3)^2$ = 13\ \mathrm{m}$$

Question 3

An eagle descends from a height of $$19.5\ \mathrm{m} at a $$constant speed of $$3.10\ \mathrm{m/s} at$$ $$20.0^\circ$$ below the horizontal. What is the time it takes to reach the water?

Accepted Answer

$$t = \frac{-19.5}{-3.10 \sin 20.0^\circ} = 18.4\ \mathrm{s}$$

Question 4

A projectile is launched from the origin with $$v_0 = 20.0$$\ \mathrm{m/s}$$ at 35.0$$^\circ$$ above the horizontal. What is the x$-position after 1.00$$\ \mathrm{s}$$?

Accepted Answer

$$x = 0 + 20.0 \cos 35.0^\circ 	imes 1.00 = 16.4\ \mathrm{m}$$

Question 5

A ball is thrown horizontally from a cliff. Which of the following statements about its acceleration is correct?

Accepted Answer

The acceleration is $$a_x = 0$$, $$a_y = -g at $$all times.

Question 6

A projectile reaches its maximum height when:

Accepted Answer

The vertical component of its velocity is zero.

Question 7

A helicopter moves horizontally at $$11\ \mathrm{m/s}$$ and accelerates upward at $$0.96\ \mathrm{m/s^2$}. $$What is the $$y-$$component of its velocity after $$5.3\ \mathrm{s}$$?

Accepted Answer

$$v_y = 0 + 0.96 	imes 5.3 = 5.1\ \mathrm{m/s}$$

Question 8

A projectile is launched from the ground with $$v_0 = 20.0$$\ \mathrm{m/s}$$ at 35.0$$^\circ$$. What is the maximum height it reaches?

Accepted Answer

$$y = \frac{(v_{0y})^2$}{2g} = \frac{(11.5)^2$}{2 	imes 9.81} = 6.74\ \mathrm{m}$$

Question 9

A ball is thrown horizontally from a height of $$10\ \mathrm{m}$$ with a speed of $$5\ \mathrm{m/s}. $$How far from the base of the cliff does it land? (Neglect air resistance, $$g = 9.81\ \mathrm{m/s^2$})$$

Accepted Answer

First, $$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 10}{9.81}} = 1.43\ \mathrm{s}$$; then $$x = v_{0x} t = 5 	imes 1.43 = 7.15\ \mathrm{m}$$

Question 10

A projectile is launched from the ground at $$v_0 = 20.0$$\ \mathrm{m/s}$$, $$	heta = 35.0^\circ$$. At what time does it reach its maximum height?

Accepted Answer

$$t = \frac{v_{0y}}{g} = \frac{11.5}{9.81} = 1.17\ \mathrm{s}$$

Question 11

A ball is thrown at $$20.0\ \mathrm{m/s} at$$ $$35.0^\circ$$ above the horizontal. What is the velocity vector at $$t = 1.50\ \mathrm{s}$$?

Accepted Answer

$$\vec{v} = (16.4\ \mathrm{m/s}) \hat{x} + (-3.22\ \mathrm{m/s}) \hat{y}$$

Question 12

A helicopter starts at the origin and moves with $$v_{0x} = 11\ \mathrm{m/s}$$ and $$a_y = 0.96\ \mathrm{m/s^2$}. $$What is its displacement vector after $$6.1\ \mathrm{s}$$?

Accepted Answer

$$\Delta \vec{r} = (67\ \mathrm{m}) \hat{x} + (18\ \mathrm{m}) \hat{y}$$

Question 13

A projectile is launched from the ground. At what two times is it at half its maximum height?

Accepted Answer

At $$t_1 = 0.34$$\ \mathrm{s}$$ and t_2$ = 2.00\ \mathrm{s}$$, because the projectile passes the same height twice: once going up and once coming down.

Question 14

Which of the following best describes the path of a projectile under the influence of gravity (neglecting air resistance)?

Accepted Answer

A parabola

Question 15

A ball is dropped from rest and another is thrown horizontally from the same height. Which statement is true about their vertical motion?

Accepted Answer

Both balls have the same vertical acceleration and hit the ground at the same time.

Two-Dimensional Kinematics: Motion, Projectile Motion, and Applications

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