Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$Which equation gives the maximum height reached by the projectile?

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

Question 1

A ball is thrown horizontally from the top of a 45 m high cliff with an initial speed of 10 m/s. Neglecting air resistance, how far from the base of the cliff does the ball land? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$30.3\ \mathrm{m}$$

Question 2

A 5 kg box is pulled up a frictionless ramp inclined at $$30^\circ to $$the horizontal. What is the magnitude of the force parallel to the ramp required to move the box at constant velocity? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$24.5\ \mathrm{N}$$

Question 3

Which of the following correctly expresses Newton's Second Law for a system with constant mass?

Accepted Answer

$$\sum \vec{F} = m \vec{a}$$

Question 4

A satellite orbits Earth in a circular path. If the radius of the orbit is doubled, how does the period change? (Assume $$T^2$$ \propto $$r^3)$$

Accepted Answer

The period increases by a factor of $$2.83$$

Question 5

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which equation gives the maximum height reached by the projectile?

Accepted Answer

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

Question 6

A 70 kg astronaut weighs less on the Moon than on Earth. Which equation correctly relates the astronaut's weight $$W to $$mass $$m$$ and gravitational acceleration $$g$$?

Accepted Answer

$$W = m g$$

Question 7

A car rounds a flat curve of radius $$r at $$constant speed $$v. $$What is the required centripetal acceleration?

Accepted Answer

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

Question 8

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

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

Question 9

A pendulum completes 20 oscillations in 25 seconds. What is its period?

Accepted Answer

$$1.25\ \mathrm{s}$$

Question 10

A 2 kg object is acted on by a net force of $$10\ \mathrm{N}. $$What is its acceleration?

Accepted Answer

$$5\ \mathrm{m/s^2$}$$

Question 11

A ball is thrown at $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. What is the horizontal component of its velocity?

Accepted Answer

$$17.3\ \mathrm{m/s}$$

Question 12

A cyclist travels at a constant speed around a circular track. Which of the following statements is true?

Accepted Answer

The cyclist's velocity is changing because its direction changes.

Question 13

A 10 kg box rests on a ramp inclined at $$25^\circ. $$What is the normal force acting on the box? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$88.8\ \mathrm{N}$$

Question 14

A projectile is launched horizontally from a height $$h$$ with speed $$v_0. $$Which equation gives the time to hit the ground?

Accepted Answer

$$t = \sqrt{\dfrac{2h}{g}}$$

Question 15

A planet orbits a star with period $$T$$ and radius $$r. If $$the period is $$8$$ years, what is the ratio $$r/r_0 if$$ $$T_0 = 1$ year and r_0$ is the Earth's orbital radius? (Use T^2$ \propto r^3$)

Accepted Answer

$$4$$

Question 16

A 3 kg object is moving in a circle of radius $$2\ \mathrm{m} at$$ $$6\ \mathrm{m/s}. $$What is the required centripetal force?

Accepted Answer

$$54\ \mathrm{N}$$

Question 17

A ball is dropped from rest from a height of $$20\ \mathrm{m}. $$How long does it take to reach the ground? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.02\ \mathrm{s}$$

Question 18

A 4 kg object is at rest on a horizontal surface. What is the normal force acting on it? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$39.2\ \mathrm{N}$$

Question 19

A satellite in circular orbit has a period $$T$$ and radius $$r. If $$the radius is increased by a factor of $$3$$, by what factor does the period change?

Accepted Answer

$$5.20$$

Question 20

A ball is thrown vertically upward with speed $$v_0. $$What is the total time it spends in the air before returning to the thrower's hand?

Accepted Answer

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

Equation Sheet for Exam 2: Motion, Forces, and Orbits

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