Q: A ball is thrown horizontally from a 10 m high cliff with an initial speed of $$5\ \mathrm{m/s}. $$How long does it take to hit the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 \times 10}{9.8}} \approx 1.43\ \mathrm{s}$$

Q: A dog runs off a dock horizontally at $$8.5\ \mathrm{m/s}$$ from a height of $$0.61\ \mathrm{m}. $$How far from the dock does the dog land? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$x = v_x t = 8.5 \times \sqrt{\frac{2 \times 0.61}{9.8}} \approx 3.0\ \mathrm{m}$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_i. $$What is the time of flight over level ground?

$$\Delta t = \frac{2 v_i \sin \theta}{g}$$

Q: What is the net force acting on an object if three forces $$\vec{F}_1$$, $$\vec{F}_2$$, and $$\vec{F}_3$$ act on it?

$$\vec{F}_{\text{net}} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3$$

Question 1

A vector $$\vec{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$\vec{A}$$?

Accepted Answer

$$A = \sqrt{3^2$ + 4^2$} = 5$$

Question 2

A ball is thrown horizontally from a 10 m high cliff with an initial speed of $$5\ \mathrm{m/s}. $$How long does it take to hit the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = \sqrt{\frac{2h}{g}} = \sqrt{\frac{2 	imes 10}{9.8}} \approx 1.43\ \mathrm{s}$$

Question 3

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal and vertical motions are independent of each other.

Question 4

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

Accepted Answer

$$x = v_x t = 8.5 	imes \sqrt{\frac{2 	imes 0.61}{9.8}} \approx 3.0\ \mathrm{m}$$

Question 5

A car travels around a circular track at constant speed. Which statement is true?

Accepted Answer

The car is accelerating because its velocity direction is changing.

Question 6

A projectile is launched at an angle $$	heta$$ with initial speed $$v_i. $$What is the time of flight over level ground?

Accepted Answer

$$\Delta t = \frac{2 v_i \sin 	heta}{g}$$

Question 7

A toy car moves around a circular track at constant speed. If the speed doubles, by what factor does the centripetal acceleration change?

Accepted Answer

4

Question 8

A plane flies east at $$500\ \mathrm{km/h}$$ with a wind blowing south at $$100\ \mathrm{km/h}. $$What is the plane's speed relative to the ground?

Accepted Answer

$$v = \sqrt{500^2$ + 100^2$} = \sqrt{260000} \approx 509.9\ \mathrm{km/h}$$

Question 9

Which of the following is NOT a property of a force?

Accepted Answer

A force is always a scalar.

Question 10

A heavy red ball is dropped from rest and a yellow ball is fired horizontally from the same height at the same instant. Which hits the ground first?

Accepted Answer

They hit at the same time.

Question 11

What is the net force acting on an object if three forces $$\vec{F}_1$$, $$\vec{F}_2$$, and $$\vec{F}_3$$ act on it?

Accepted Answer

$$\vec{F}_{	ext{net}} = \vec{F}_1 + \vec{F}_2 + \vec{F}_3$$

Question 12

A projectile is launched at $$30^\circ$$ and $$60^\circ$$ with the same initial speed. Which statement is true about their ranges (horizontal distances)?

Accepted Answer

They have the same range.

Question 13

Which of the following best describes Newton’s First Law?

Accepted Answer

An object at rest remains at rest, and an object in motion remains in motion at constant velocity unless acted on by a net force.

Question 14

A runner moves at $$5\ \mathrm{m/s}$$ relative to the ground. A cyclist moves at $$5\ \mathrm{m/s} in $$the same direction. What is the runner’s velocity relative to the cyclist?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 15

A force is applied to a sled on ice, causing it to accelerate. If the force is doubled, what happens to the acceleration (assuming mass is constant)?

Accepted Answer

The acceleration doubles.

Vectors, Projectile Motion, Circular Motion, and Forces: Study Notes for Physics with Calculus

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