Q: A baseball is hit at $$44.7\ \mathrm{m/s} at an $$angle of $$20.5^\circ$$ above the horizontal. Neglecting air resistance, what is the maximum height attained by the ball?

$$\frac{(44.7 \sin 20.5^\$$circ)^2$$}{2 \times 9.8} \approx 7.3\ \mathrm{m}$$

Q: Given $$\vec{A} = (11.1)\hat{i} + (12.2)\hat{j}$$ and $$\vec{B} = (3.48)\hat{i} - (3.09)\hat{j}$$, what is the magnitude of $$2\vec{A} - \vec{B}$$?

$$\sqrt{(2 \times 11.1 - 3.48)^2$ + (2 \times 12.2 - (-3.09))^2$} \approx 32.1$$

Q: A shell is fired at $$70.0\ \mathrm{m/s} at an $$angle of $$75^\circ$$ above the horizontal. What is the time to reach its maximum height?

$$t = \frac{v_0$ \sin \theta}{g} = \frac{70.0 \sin 75^\circ}{9.8} \approx 6.77\ \mathrm{s}$$

Q: A truck is moving at $$20\ \mathrm{m/s}$$ and the driver reacts in $$0.75\ \mathrm{s}$$ before braking. The truck slows down with a constant deceleration of $$4\ \mathrm{m/s^2$}$$ until it stops. What is the total stopping distance?

$$d = v_0$ t_{reaction} + \frac{v_0$^2}{2a} = 20 \times 0.75 + \frac{(20)^2$}{2 \times 4} = 15 + 50 = 65\ \mathrm{m}$$

Q: A ball is thrown horizontally from the top of a parking garage and lands $$45.0\ \mathrm{m}$$ from the base. If the ball was in the air for $$3.0\ \mathrm{s}$$, what is the height of the garage?

$$h = \frac{1}{2} g t^2$ = \frac{1}{2} \times 9.8 \times (3.0)^2$ = 44.1\ \mathrm{m}$$

Q: A car accelerates from rest at $$3.0\ \mathrm{m/s^2$}$$ for $$8.0\ \mathrm{s}. $$What is its final velocity?

$$v = at = 3.0 \times 8.0 = 24.0\ \mathrm{m/s}$$

Q: A projectile is launched at $$30^\circ$$ above the horizontal with a speed of $$20\ \mathrm{m/s}. $$What is the range of the projectile (neglecting air resistance)?

$$R = \frac{v_0$^2 \sin 2\theta}{g} = \frac{(20)^2$ \sin 60^\circ}{9.8} \approx 35.3\ \mathrm{m}$$

Question 1

A car travels 94 km per minute. What is its speed in meters per second?

Accepted Answer

$$1566.67\ \mathrm{m/s}$$

Question 2

Vector $$\vec{A} is$$ $$(6, 4)$$ and vector $$\vec{B} is$$ $$(6, -2). $$What is the magnitude of $$\vec{A} + \vec{B}$$?

Accepted Answer

$$\sqrt{(6+6)^2$ + (4+(-2))^2$} = \sqrt{144 + 4} = \sqrt{148} \approx 12.17$$

Question 3

A person walks 40 m east, then 25 m west, and finally 10 m east. What is their net displacement from the starting point?

Accepted Answer

$$25\ \mathrm{m}$$\ east

Question 4

A motorcycle is moving at $$90\ \mathrm{km/h}$$ and comes to a stop in $$5\ \mathrm{s}. $$What is its acceleration?

Accepted Answer

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

Question 5

A soccer ball is kicked at an angle of $$42^\circ$$ above the horizontal with an initial speed of $$18\ \mathrm{m/s}. $$What is the vertical component of the initial velocity?

Accepted Answer

$$18 \sin 42^\circ \approx 12.04\ \mathrm{m/s}$$

Question 6

A car travels $$23.1\ \mathrm{m} in $$the positive $$x-$$direction over $$24.2\ \mathrm{s}. $$What is its average velocity?

Accepted Answer

$$0.955\ \mathrm{m/s}$$

Question 7

A baseball is hit at $$44.7\ \mathrm{m/s} at an $$angle of $$20.5^\circ$$ above the horizontal. Neglecting air resistance, what is the maximum height attained by the ball?

Accepted Answer

$$\frac{(44.7 \sin 20.5^\$$circ)^2$$}{2 	imes 9.8} \approx 7.3\ \mathrm{m}$$

Question 8

Given $$\vec{A} = (11.1)\hat{i} + (12.2)\hat{j}$$ and $$\vec{B} = (3.48)\hat{i} - (3.09)\hat{j}$$, what is the magnitude of $$2\vec{A} - \vec{B}$$?

Accepted Answer

$$\sqrt{(2 	imes 11.1 - 3.48)^2$ + (2 	imes 12.2 - (-3.09))^2$} \approx 32.1$$

Question 9

A car starts from rest and accelerates uniformly at $$2.0\ \mathrm{m/s^2$}$$ for $$10\ \mathrm{s}$$, then continues at constant speed for $$50\ \mathrm{s}$$, and finally decelerates at $$4.0\ \mathrm{m/s^2$}$$ until it stops. What is the total distance traveled?

Accepted Answer

$$100\ \mathrm{m} + 500\ \mathrm{m} + 50\ \mathrm{m} = 650\ \mathrm{m}$$

Question 10

A shell is fired at $$70.0\ \mathrm{m/s} at an $$angle of $$75^\circ$$ above the horizontal. What is the time to reach its maximum height?

Accepted Answer

$$t = \frac{v_0$ \sin 	heta}{g} = \frac{70.0 \sin 75^\circ}{9.8} \approx 6.77\ \mathrm{s}$$

Question 11

A truck is moving at $$20\ \mathrm{m/s}$$ and the driver reacts in $$0.75\ \mathrm{s}$$ before braking. The truck slows down with a constant deceleration of $$4\ \mathrm{m/s^2$}$$ until it stops. What is the total stopping distance?

Accepted Answer

$$d = v_0$ t_{reaction} + \frac{v_0$^2}{2a} = 20 	imes 0.75 + \frac{(20)^2$}{2 	imes 4} = 15 + 50 = 65\ \mathrm{m}$$

Question 12

A ball is thrown horizontally from the top of a parking garage and lands $$45.0\ \mathrm{m}$$ from the base. If the ball was in the air for $$3.0\ \mathrm{s}$$, what is the height of the garage?

Accepted Answer

$$h = \frac{1}{2} g t^2$ = \frac{1}{2} 	imes 9.8 	imes (3.0)^2$ = 44.1\ \mathrm{m}$$

Question 13

A car accelerates from rest at $$3.0\ \mathrm{m/s^2$}$$ for $$8.0\ \mathrm{s}. $$What is its final velocity?

Accepted Answer

$$v = at = 3.0 	imes 8.0 = 24.0\ \mathrm{m/s}$$

Question 14

A projectile is launched at $$30^\circ$$ above the horizontal with a speed of $$20\ \mathrm{m/s}. $$What is the range of the projectile (neglecting air resistance)?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2	heta}{g} = \frac{(20)^2$ \sin 60^\circ}{9.8} \approx 35.3\ \mathrm{m}$$

Question 15

A vector $$\vec{C}$$ satisfies $$\vec{A} - \vec{B} + 5.5\vec{C} = 0$$, where $$\vec{A} = (5.6, 15.7)$$ and $$\vec{B} = (14.3, -18.4). $$What is the $$x-$$component of $$\vec{C}$$?

Accepted Answer

$$C_x = \frac{B_x - A_x}{5.5} = \frac{14.3 - 5.6}{5.5} = 1.582$$

Question 16

A car travels $$23.1\ \mathrm{m} in$$ $$24.2\ \mathrm{s}$$, then brakes to a stop in $$5.33\ \mathrm{s}. If $$the car's initial velocity is the average velocity during the first interval, what is the car's acceleration during braking?

Accepted Answer

$$a = \frac{0 - 0.955}{5.33} = -0.179\ \mathrm{m/s^2$}$$

Question 17

A fireworks shell is shot into the air at $$70.0\ \mathrm{m/s} at$$ $$75^\circ$$ above the horizontal. If it explodes at its highest point, what is the horizontal displacement when it explodes?

Accepted Answer

$$x = v_0$ \cos 	heta 	imes t_{up} = 70.0 \cos 75^\circ 	imes 6.77 \approx 122.5\ \mathrm{m}$$

Vectors and Kinematics: Study Notes for College Physics

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