Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the formula for the range $$R ($$horizontal distance traveled before landing) on level ground?

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

Q: A girl swings on a rope and lets go with an initial velocity of $$2.25\ \mathrm{m/s} at$$ $$35.0^\circ$$ above the horizontal, remaining in flight for $$0.616\ \mathrm{s}. $$How high above the water was she when she let go?

$$h = v_0$ \sin \theta \cdot t - \frac{1}{2}gt^2$

Question 1

A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following statements is TRUE about the horizontal and vertical components of its velocity during flight (neglecting air resistance)?

Accepted Answer

The horizontal component remains constant, while the vertical component changes due to gravity.

Question 2

A Mars rover moves along a path as shown in the diagram. At $$t = 0.0\ \mathrm{s}$$, its velocity is downward and to the right. At $$t = 2.0\ \mathrm{s}$$, its velocity is upward and to the left. What is the direction of the average acceleration vector during this interval?

Accepted Answer

Up and to the left

Question 3

A crow flying horizontally at $$2.70\ \mathrm{m/s}$$ drops a clam, which lands $$2.10\ \mathrm{s}$$ later. What is the vertical component of the clam's velocity just before it lands? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$v_y = -20.6\ \mathrm{m/s}$$

Question 4

A soccer ball is kicked with an initial speed of $$10.2\ \mathrm{m/s} at$$ $$25^\circ$$ above the horizontal. What is the horizontal component of its velocity?

Accepted Answer

$$10.2 \cos 25^\circ$$

Question 5

A pumpkin is thrown horizontally from a $$9.0\ \mathrm{m}$$ high tower and lands $$3.5\ \mathrm{m}$$ away. What launch speed is needed to hit the bullseye? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_0$$ = \frac{3.5}{\sqrt{2h/g}}$$

Question 6

Which of the following best describes the speed of a projectile thrown upward at $$10\ \mathrm{m/s} at$$ $$60^\circ$$ above the horizontal, as a function of time until it returns to its original height?

Accepted Answer

Gravity decreases the ball’s speed until it reaches the peak height, then increases it as it falls.

Question 7

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the formula for the range $$R ($$horizontal distance traveled before landing) on level ground?

Accepted Answer

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

Question 8

A girl swings on a rope and lets go with an initial velocity of $$2.25\ \mathrm{m/s} at$$ $$35.0^\circ$$ above the horizontal, remaining in flight for $$0.616\ \mathrm{s}. $$How high above the water was she when she let go?

Accepted Answer

$$h = v_0$ \sin 	heta \cdot t - \frac{1}{2}gt^2$

Question 9

Which of the following is TRUE about uniform circular motion?

Accepted Answer

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

Question 10

A boat heads straight across a river with a speed of $$6.1\ \mathrm{m/s}$$ relative to the water. The river flows downstream at $$1.4\ \mathrm{m/s}. $$What is the magnitude of the boat's velocity relative to the ground?

Accepted Answer

$$\sqrt{6.1^2$ + 1.4^2$}\ \mathrm{m/s}$$

Question 11

Which of the following is the correct formula for centripetal acceleration $$a_c$$ for an object moving in a circle of radius $$r at $$speed $$v$$?

Accepted Answer

$$a_c = \frac{v^2$}{r}$$

Question 12

A book is dropped inside a descending elevator moving at constant speed $$v_0. $$What is the time $$T it $$takes for the book to fall a distance $$h to $$the floor?

Accepted Answer

$$T = \sqrt{\frac{2h}{g}}$$

Question 13

Which of the following is a correct statement about Galilean relativity for velocities?

Accepted Answer

Velocities add as $$\vec{v}_{pg} = \vec{v}_{pt} + \vec{v}_{tg}$$

Question 14

A projectile is launched at an angle $$	heta$$ such that its range $$R$$ and maximum height $$h$$ are equal. What is the value of $$	heta$$?

Accepted Answer

$$	heta = 63.4^\circ$$

Question 15

Which of the following is the SI unit for angular displacement?

Accepted Answer

Radian

Question 16

A volcano on Io ejects lava to a maximum height of $$2.00 	imes 10^5$\ \mathrm{m}$$ with gravity $$g_{Io} = 1.80\ \mathrm{m/s^2$}. $$What is the initial speed of the lava?

Accepted Answer

$$v_0$$ = \sqrt{2gh}$$

Question 17

Which of the following is TRUE about the independence of motion in projectile motion?

Accepted Answer

The x- and y-direction motions are independent and can be analyzed separately.

Motion in Two or Three Dimensions: Position, Velocity, Acceleration, and Projectile Motion

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