Q: A projectile is launched from ground level with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for its maximum range (neglecting air resistance)?

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

Question 1

A ball is thrown horizontally from the top of a building while another ball is dropped vertically from the same height. Neglecting air resistance, which statement is true about the time it takes for both balls to hit the ground?

Accepted Answer

Both balls hit the ground at the same time.

Question 2

Which of the following best describes the direction of the velocity vector for an object moving in a circle at constant speed?

Accepted Answer

It is always tangent to the circle.

Question 3

A dog runs off a dock that is 0.61 m above the water at a speed of 8.5 m/s. How far from the dock does the dog land? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.0\ \mathrm{m}$$

Question 4

A grasshopper jumps a horizontal distance of $$0.76\ \mathrm{m} at $$the optimal angle for maximum range. What is the minimum speed required for the jump? (Use $$g = 9.8\ \mathrm{m/s^2$}$$ and optimal angle $$= 45^	ext{o})$$

Accepted Answer

$$3.9\ \mathrm{m/s}$$

Question 5

A car moves around a circular track at a constant speed. What is true about its acceleration?

Accepted Answer

The acceleration points toward the center of the circle.

Question 6

A runner moves at $$5\ \mathrm{m/s}$$ relative to Amy, and Amy moves at $$-15\ \mathrm{m/s}$$ relative to Carlos. What is the runner's velocity relative to Carlos?

Accepted Answer

$$-10\ \mathrm{m/s}$$

Question 7

A projectile is launched from ground level with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for its maximum range (neglecting air resistance)?

Accepted Answer

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

Question 8

A plane is flying due east at $$500\ \mathrm{mph}$$, but there is a wind blowing due south at $$100\ \mathrm{mph}. $$What is the plane's speed relative to the ground?

Accepted Answer

$$510\ \mathrm{mph}$$

Question 9

A ball is launched at $$v_0 at$$ $$30^	ext{o}$$ above the horizontal. Another ball is launched at the same speed but at $$60^	ext{o}. $$Both land on level ground. Which ball spends more time in the air?

Accepted Answer

The ball launched at $$60^	ext{o}.$$

Question 10

A commercial ultracentrifuge rotates at $$100,000\ \mathrm{rpm}$$ with a sample chamber $$0.10\ \mathrm{m}$$ from the axis. What is the centripetal acceleration in terms of $$g$$ ($$g = 9.8\ \mathrm{m/s^2$}$$)?

Accepted Answer

$$100,000g$$

Question 11

A speed skater moves around a curve of radius $$11\ \mathrm{m} at a $$speed of $$30\ \mathrm{m/s}. $$What is the magnitude of the centripetal acceleration?

Accepted Answer

$$90\ \mathrm{m/s^2$}$$

Question 12

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal velocity is constant (neglecting air resistance).

Question 13

A golf ball is hit at $$30^	ext{o}$$ above the horizontal with initial speed $$v_0. $$Another ball is hit at the same angle but with twice the speed. If the first ball lands at distance $$d$$, how far does the second ball land?

Accepted Answer

$$4d$$

Question 14

Which of the following best describes the acceleration of an object moving in a circle at constant speed?

Accepted Answer

It points toward the center and has magnitude $$a = \dfrac{v^2$}{r}.$$

Question 15

If a car doubles its speed while moving around a circular track of fixed radius, by what factor does its centripetal acceleration change?

Accepted Answer

It quadruples.

Question 16

A skydiver jumps out of a plane 1000 m above the ground and quickly reaches a constant vertical speed of $$35\ \mathrm{m/s}. If a $$wind blows horizontally at $$7\ \mathrm{m/s}$$, what is the horizontal displacement of the skydiver when he lands?

Accepted Answer

$$200\ \mathrm{m}$$

Question 17

Which of the following is the correct formula for average acceleration in two dimensions?

Accepted Answer

$$\vec{a} = \dfrac{\vec{v}_f - \vec{v}_i}{t_f - t_i}$$

Question 18

In projectile motion, what is the vertical velocity of the projectile at the highest point of its trajectory?

Accepted Answer

It is zero.

Question 19

A conveyor belt moves at $$2\ \mathrm{m/s} to $$the right. A mouse runs at $$1\ \mathrm{m/s} to $$the left on the belt. What is the mouse's speed relative to the floor?

Accepted Answer

$$1\ \mathrm{m/s} to $$the right

Motion in Two Dimensions: Vectors, Acceleration, and Projectile Motion

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