Q: A projectile is launched from the ground with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following equations gives the time of flight until it returns to the ground?

$$t = \dfrac{2 v_0$ \sin \theta}{g}$$

Question 1

A small bag of sand is released from an ascending hot-air balloon whose constant, upward velocity is 8.25 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 $$g = 9.8\ \mathrm{m/s^2$}$$, upward is positive.)

Accepted Answer

$$t = 8.1\ \mathrm{s}$$

Question 2

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

Accepted Answer

The acceleration always points toward the center of the circle.

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 equations gives the time of flight until it returns to the ground?

Accepted Answer

$$t = \dfrac{2 v_0$ \sin 	heta}{g}$$

Question 4

A car travels around a curve at a steady 45 mph. Which vector shows the direction of the car’s acceleration?

Accepted Answer

Toward the center of the curve.

Question 5

A mouse runs straight across a conveyor belt moving at 3 m/s. The mouse runs at 4 m/s relative to the belt, perpendicular to the belt’s motion. What is the mouse’s speed relative to the floor?

Accepted Answer

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

Question 6

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the maximum range (horizontal distance) achieved, and at what angle does this occur?

Accepted Answer

Maximum range is $$\dfrac{v_0$^2}{g} at$$ $$45^\circ.$$

Question 7

A skydiver jumps out of an airplane 1000 m directly above his desired landing spot. He falls at 35 m/s and there is a breeze blowing at 7 m/s to the west. What is his displacement from the target when he lands?

Accepted Answer

$$200\ \mathrm{m}$$ west

Question 8

A grasshopper jumps a distance of $$0.76\ \mathrm{m} at an $$angle of $$45^\circ. $$What is the initial speed of the jump? (Assume $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$v_0 = 2.7$$\ \mathrm{m/s}$$

Question 9

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

$$4$$

Question 10

A ball is thrown horizontally from a cliff with speed $$v_0. $$Which of the following statements is true about its motion?

Accepted Answer

The horizontal and vertical motions are independent.

Question 11

Two projectiles are launched from the same height with the same speed but at different angles. Which hits the ground first (ignore air resistance)?

Accepted Answer

They hit the ground at the same time.

Question 12

A runner moves at $$5\ \mathrm{m/s}$$ east relative to the ground, and a conveyor belt moves at $$2\ \mathrm{m/s}$$ north relative to the ground. What is the runner’s speed relative to the ground if he runs north on the belt at $$3\ \mathrm{m/s}$$ relative to the belt?

Accepted Answer

$$\sqrt{2^2$ + 3^2$} = 3.6\ \mathrm{m/s}$$

Question 13

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

Accepted Answer

$$v = 2800\ \mathrm{m/s}$$

Question 14

Which of the following is true about the velocity and acceleration vectors for an object in uniform circular motion?

Accepted Answer

The velocity is tangent to the circle, and the acceleration points toward the center.

Question 15

A ball is thrown horizontally from a 20 m high cliff with a speed of $$5\ \mathrm{m/s}. $$How far from the base of the cliff does the ball land? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$14.3\ \mathrm{m}$$

Question 16

A runner moves at $$6\ \mathrm{m/s}$$ north relative to the ground. A wind blows at $$8\ \mathrm{m/s}$$ east. What is the runner’s speed relative to the ground?

Accepted Answer

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

Kinematics: Sandbag Released from Ascending Balloon

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