Q: A vector $$\vec{v}$$ has $$v_x = 20\ \mathrm{m/s}$$ and $$v_y = 5.0\ \mathrm{m/s}. $$What is the magnitude and direction of $$\vec{v}$$?

$$|\vec{v}| = 20.6\ \mathrm{m/s}$$,\ \theta = 14^\circ$$ above the x$-axis

Q: A solar sail spacecraft experiences a force of $$1.12\ \mathrm{mN} on a$$ $$200\ \mathrm{m^2$}$$ sail. If the force increases by $$20\%$$ after 6 months, what is the new acceleration if the spacecraft mass is $$1000\ \mathrm{kg}$$?

$$a = 1.34\times 10$$^{-6}$$\ \mathrm{m/s^2$}$$

Question 1

A car accelerates uniformly from 0 to 60 mph in 10 seconds. What is the car's acceleration in SI units ($$\mathrm{m/s^2$}$$)?

Accepted Answer

$$a = 2.68\ \mathrm{m/s^2$}$$

Question 2

A driver traveling at $$20\ \mathrm{m/s}$$ sees an obstacle $$50\ \mathrm{m}$$ ahead. Her reaction time is $$0.50\ \mathrm{s}$$ and her car's maximum deceleration is $$6.0\ \mathrm{m/s^2$}. $$Can she stop in time to avoid a collision?

Accepted Answer

No, she will not stop in time; she will hit the obstacle.

Question 3

A paintball gun is aimed horizontally at a target $$50\ \mathrm{m}$$ away. The paintball hits the target $$2.0\ \mathrm{m}$$ below the aim point. What was the paintball's flight time?

Accepted Answer

$$t = 0.64\ \mathrm{s}$$

Question 4

A gannet dives from rest and hits the water at $$32\ \mathrm{m/s}. $$What height did it dive from? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = 52\ \mathrm{m}$$

Question 5

A man pulls an empty wagon causing it to accelerate at $$1.4\ \mathrm{m/s^2$}. If $$the wagon now contains a child whose mass is three times that of the wagon, what is the new acceleration if the same force is applied?

Accepted Answer

$$a = 0.35\ \mathrm{m/s^2$}$$

Question 6

A squid of mass $$1.5\ \mathrm{kg}$$ accelerates at $$3.0\ \mathrm{m/s^2$} by $$ejecting $$0.15\ \mathrm{kg} of $$water. What is the magnitude of the thrust force on the squid?

Accepted Answer

$$F = 4.5\ \mathrm{N}$$

Question 7

A baseball ($$0.145\ \mathrm{kg}) is $$hit and accelerates from rest to $$30\ \mathrm{m/s} in$$ $$0.0020\ \mathrm{s}. $$What is the average force exerted on the ball?

Accepted Answer

$$F = 2175\ \mathrm{N}$$

Question 8

A car is skidding to a stop on a level road. Which of the following is an action-reaction pair according to Newton's third law?

Accepted Answer

The force of the road on the tires and the force of the tires on the road.

Question 9

A paintball leaves the barrel of a gun horizontally and hits a target $$50\ \mathrm{m}$$ away, $$2.0\ \mathrm{m}$$ below the aim point. What was the paintball's speed as it left the barrel?

Accepted Answer

$$v = 78\ \mathrm{m/s}$$

Question 10

On the Apollo 14 mission, Alan Shepard hit a golf ball on the moon with a speed of $$25\ \mathrm{m/s} at an $$angle $$30^\circ$$ above the horizontal. How long was the ball in flight? (Moon's $$g = 1.67\ \mathrm{m/s^2$})$$

Accepted Answer

$$t = 15\ \mathrm{s}$$

Question 11

A snail ejects water from its shell to escape a predator. If the mass of water ejected is $$2.5\ \mathrm{g}$$ and the velocity is $$0.4\ \mathrm{m/s}$$, what is the magnitude of the thrust force if the ejection lasts $$0.2\ \mathrm{s}$$?

Accepted Answer

$$F = 0.005\ \mathrm{N}$$

Question 12

A vector $$\vec{A}$$ has magnitude $$3.0\ \mathrm{m}$$ and points $$20^\circ$$ south of east. What are its $$x$$ and $$y$$ components?

Accepted Answer

$$A_x = 2.82\ \mathrm{m},\ A_y = -1.03\ \mathrm{m}$$

Question 13

A child safety seat is installed facing the rear of a car. In a head-on collision, why is the infant much safer in this orientation?

Accepted Answer

The seat supports the infant's head and neck, reducing whiplash and distributing forces over a larger area.

Question 14

A car travels $$60\ \mathrm{mph}$$ for $$10\ \mathrm{s}. $$How far does it travel in SI units?

Accepted Answer

$$d = 268\ \mathrm{m}$$

Question 15

A vector $$\vec{v}$$ has $$v_x = 20\ \mathrm{m/s}$$ and $$v_y = 5.0\ \mathrm{m/s}. $$What is the magnitude and direction of $$\vec{v}$$?

Accepted Answer

$$|\vec{v}| = 20.6\ \mathrm{m/s}$$,\ 	heta = 14^\circ$$ above the x$-axis

Question 16

A solar sail spacecraft experiences a force of $$1.12\ \mathrm{mN} on a$$ $$200\ \mathrm{m^2$}$$ sail. If the force increases by $$20\%$$ after 6 months, what is the new acceleration if the spacecraft mass is $$1000\ \mathrm{kg}$$?

Accepted Answer

$$a = 1.34	imes 10$$^{-6}$$\ \mathrm{m/s^2$}$$

Question 17

A squid ejects $$0.15\ \mathrm{kg} of $$water at $$30\ \mathrm{m/s^2$}$$ acceleration. What is the force experienced by the water?

Accepted Answer

$$F = 4.5\ \mathrm{N}$$

Question 18

In downtown Chicago, east-west blocks are $$400\ \mathrm{ft}$$ long and north-south blocks are $$280\ \mathrm{ft}$$ long. If a taxi drives 3 blocks north, 2 blocks east, and 2 blocks south, what is the straight-line distance from its starting point?

Accepted Answer

$$d = 800\ \mathrm{ft}$$

Kinematics and Dynamics: Study Notes and Problem Guide

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