Q: A projectile is launched from the ground with an initial velocity $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following correctly describes the horizontal and vertical components of the initial velocity?

$$v_{0x} = v_0$ \cos \theta$$, $$v_{0y} = v_0$ \sin \theta$$

Q: A ball is thrown with an initial velocity of $$15\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the time of flight until it lands back at the same height? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \dfrac{2 v_0$ \sin \theta}{g} = \dfrac{2 \times 15 \times 0.5}{9.8} = 1.53\ \mathrm{s}$$

Q: A glass of milk is kicked at an angle of $$40^\circ to $$the horizontal and lands $$100\ \mathrm{m}$$ away. What initial speed is required? (Assume $$\Delta y = 0$$ and $$g = 9.8\ \mathrm{m/s^2$})$$

$$v_0$$ = \sqrt{\dfrac{g \Delta x}{\sin 2\theta}} = \sqrt{\dfrac{9.8 \times 100}{\sin 80^\circ}} = 31.5\ \mathrm{m/s}$$

Question 1

A projectile is launched from the ground with an initial velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following correctly describes the horizontal and vertical components of the initial velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$, $$v_{0y} = v_0$ \sin 	heta$$

Question 2

Refer to the first image (projectile motion diagram). At point C, what is the value of the vertical component of the velocity $$v_y$$?

Accepted Answer

$$v_y = 0$$

Question 3

A ball is thrown with an initial velocity of $$15\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the time of flight until it lands back at the same height? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \dfrac{2 v_0$ \sin 	heta}{g} = \dfrac{2 	imes 15 	imes 0.5}{9.8} = 1.53\ \mathrm{s}$$

Question 4

In the second image, at the point marked X, what is the direction of the velocity vector?

Accepted Answer

The velocity is tangent to the trajectory, pointing up and to the right.

Question 5

In the third image, at the point marked X, what is the direction of the acceleration vector?

Accepted Answer

The acceleration is straight down.

Question 6

A vector has components $$K_x = 6\ \mathrm{m}$$ and $$K_y = -8\ \mathrm{m}. $$What is the magnitude of the vector $$K$$?

Accepted Answer

$$K = \sqrt{K_x^2$ + K_y^2$} = \sqrt{36 + 64} = 10\ \mathrm{m}$$

Question 7

A prince throws a rock from a castle wall with an initial velocity of $$12\ \mathrm{m/s} at$$ $$42^\circ$$ above the horizontal. The rock lands $$9.5\ \mathrm{m}$$ below the initial height. What is the vertical component of the velocity just before landing?

Accepted Answer

$$v_{yf} = \sqrt{v_{yi}^2 + 2a\Delta y} = \sqrt{8.0^2$ + 2(-9.8)(-9.5)} = 15.8\ \mathrm{m/s}$$ downward

Question 8

Which of the following statements about projectile motion is correct (neglecting air resistance)?

Accepted Answer

The horizontal velocity remains constant throughout the motion.

Question 9

A merry-go-round horse travels at constant speed around a circle of circumference $$31.4\ \mathrm{m} in$$ $$20.0\ \mathrm{s}. $$What is the magnitude of its velocity?

Accepted Answer

$$v = \dfrac{31.4}{20.0} = 1.57\ \mathrm{m/s}$$

Question 10

A glass of milk is kicked at an angle of $$40^\circ to $$the horizontal and lands $$100\ \mathrm{m}$$ away. What initial speed is required? (Assume $$\Delta y = 0$$ and $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_0$$ = \sqrt{\dfrac{g \Delta x}{\sin 2	heta}} = \sqrt{\dfrac{9.8 	imes 100}{\sin 80^\circ}} = 31.5\ \mathrm{m/s}$$

Question 11

Which of the following best describes the acceleration of an object in uniform circular motion?

Accepted Answer

The acceleration is always directed toward the center of the circle.

Question 12

A vector $$A$$ makes an angle $$	heta$$ with the negative $$y-$$axis. What is the length of the component of $$A$$ along the $$x-$$axis?

Accepted Answer

$$A \sin 	heta$$

Question 13

A ball is thrown horizontally from a balcony $$22\ \mathrm{m}$$ above the ground with a speed of $$12\ \mathrm{m/s}. $$How long does it take to hit the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}} = \sqrt{\dfrac{2 	imes 22}{9.8}} = 2.12\ \mathrm{s}$$

Question 14

A vector has components $$K_x = 6\ \mathrm{m}$$ and $$K_y = -8\ \mathrm{m}. $$What is the angle between $$K$$ and the $$+x$$ axis?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\dfrac{K_y}{K_x}ight) = 	an$$^{-1}$$\left(\dfrac{-8}{6}ight) = -53^\circ$$

Question 15

Which of the following is true about the horizontal and vertical motions of a projectile (neglecting air resistance)?

Accepted Answer

The horizontal and vertical motions are independent of each other.

Question 16

A ball is thrown at $$11.0\ \mathrm{m/s} at$$ $$39^\circ$$ above the horizontal from a height of $$2.0\ \mathrm{m}. If it $$lands $$10.0\ \mathrm{m}$$ away, what is its height when it reaches the friend?

Accepted Answer

$$y = 3.4\ \mathrm{m}$$ above the ground

Question 17

Which kinematic equation would you use to find the vertical displacement $$\Delta y of a $$projectile given initial vertical velocity $$v_{yi}$$, time $$\Delta t$$, and acceleration $$a$$?

Accepted Answer

$$\Delta y = v_{yi} \Delta t + \dfrac{1}{2} a \Delta t^2$

2D Kinematics and Projectile Motion: Study Notes

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