Question 1

A small bag of sand is released from an ascending hot-air balloon whose constant, upward velocity is 8.5 m/s. If the balloon is 220 m above the ground when the sandbag is released, how much time does it take for the sandbag to reach the ground? (Take upward as positive and $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$t = 8.0\ \mathrm{s}$$

Question 2

Which of the following best describes the acceleration of a car moving at constant speed around a circular track?

Accepted Answer

The acceleration points toward the center of the circle at all points.

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 statements is true about the projectile's horizontal and vertical motions?

Accepted Answer

The horizontal motion is at constant velocity, and the vertical motion is at constant acceleration.

Question 4

A grasshopper jumps a distance of $$0.76\ \mathrm{m}$$ from a standing start. If it takes off at the optimal angle for maximum range, what is the initial speed of the jump? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v_0 = 3.1$$\ \mathrm{m/s}$$

Question 5

A toy car moves around a circular track at constant speed. It suddenly doubles its speed. By what factor does the centripetal acceleration change?

Accepted Answer

It increases by a factor of $$4.$$

Question 6

A factory conveyor belt rolls at $$3\ \mathrm{m/s}. A $$mouse sees a piece of cheese directly across the belt and heads straight for the cheese at $$4\ \mathrm{m/s}. $$What is the mouse’s speed relative to the factory floor?

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 7

Two projectiles are launched from the same point over level ground with the same speed but at different angles. Which hits the ground first? (Ignore air resistance.)

Accepted Answer

They hit at the same time.

Question 8

A runner moves at $$5\ \mathrm{m/s}$$ east relative to the ground. A wind blows at $$3\ \mathrm{m/s}$$ north relative to the ground. What is the runner’s speed relative to the ground?

Accepted Answer

$$5.8\ \mathrm{m/s}$$

Question 9

A car is traveling around a curve at a steady $$45\ \mathrm{mph}. $$Which vector shows the direction of the car’s acceleration?

Accepted Answer

Toward the center of the curve.

Question 10

A skydiver jumps out of an airplane $$1000\ \mathrm{m}$$ directly above his desired landing spot. He falls at $$35\ \mathrm{m/s}$$ and there is a breeze blowing at $$7\ \mathrm{m/s} to $$the west. What is the magnitude of his velocity relative to the ground?

Accepted Answer

$$35.7\ \mathrm{m/s}$$

Question 11

A ball is thrown horizontally from a $$20\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How far from the base of the cliff does the ball land? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$14.3\ \mathrm{m}$$

Question 12

A commercial ultracentrifuge rotates at $$100,000\ \mathrm{rpm}$$ and creates an acceleration of $$800,000g. $$What is the speed of an object traveling under these conditions? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$8860\ \mathrm{m/s}$$

Question 13

Two golf balls are hit from the same point on a flat field at an angle of $$30^\circ$$ above the horizontal. Ball 2 has twice the initial speed of ball 1. If ball 1 lands a distance $$d_1$$ from the initial point, at what distance $$d_2$$ does ball 2 land? (Neglect air resistance.)

Accepted Answer

$$d_2 = 4d_1$

Question 14

A particle changes direction with no change of speed at point 2 in a motion diagram. What is the direction of the acceleration at point 2?

Accepted Answer

Perpendicular to the velocity vector, toward the center of curvature.

Question 15

A plane leaves Chicago flying due east at $$500\ \mathrm{mph}. $$The wind is blowing to the south at $$100\ \mathrm{mph}. $$What is the plane’s velocity relative to the ground?

Accepted Answer

$$\sqrt{500^2$ + 100^2$}\ \mathrm{mph}$$

Kinematics: Sandbag Released from Ascending Balloon

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