Q: After converting $$B to $$feet ($$1\text{ m} = 3.281\text{ ft}$$), what is the magnitude of $$B in $$feet?

$$28 \times 3.281 = 91.868\text{ ft}$$

Q: If you drive east at $$30\text{ mph}$$ for $$2$$ hours and then north at $$30\text{ m/s}$$ for another $$2$$ hours, what is your total displacement from the starting point? (Use $$1\text{ mph} = 0.447\text{ m/s})$$

Total displacement is $$\sqrt{(96,600\text{ m})^2$ + (216,000\text{ m})^2$}$$

Q: You start from rest and accelerate from $$30\text{ mph} to$$ $$30\text{ m/s} in$$ $$1$$ minute. What is your acceleration in $$\text{m/s}^2$$? ($$1\text{ mph} = 0.447\text{ m/s})$$

$$a = \frac{30\text{ m/s} - 13.41\text{ m/s}}{60\text{ s}} = 0.2765\text{ m/s}^2$$

Q: A projectile is launched at $$23\text{ m/s} at an $$angle of $$72^\circ. $$What is the vertical component of its initial velocity?

$$v_{0y} = 23 \times \sin(72^\circ) = 21.85\text{ m/s}$$

Q: For the projectile launched at $$23\text{ m/s} at$$ $$72^\circ$$, what is the maximum height $$y_{max}$$ reached? (Use $$g = 9.8\text{ m/s}^2)$$

$$y_{max} = \frac{(21.85)^2$}{2 \times 9.8} = 24.34\text{ m}$$

Q: What is the total time of flight $$t_f$$ for the projectile launched at $$23\text{ m/s} at$$ $$72^\circ$$?

$$t_f = \frac{2 \times 21.85}{9.8} = 4.46\text{ s}$$

Q: What is the horizontal range $$\Delta x$$ for the projectile launched at $$23\text{ m/s} at$$ $$72^\circ$$?

$$\Delta x = 7.12 \times 4.46 = 31.77\text{ m}$$

Q: If a vector $$A$$ has magnitude $$28\text{ ft}$$ and direction $$48^\circ$$, what are its $$x$$ and $$y$$ components?

$$A_x = 28 \times \cos(48^\circ) = 18.75\text{ ft}$$, $$A_y = 28 \times \sin(48^\circ) = 20.81\text{ ft}$$

Question 1

A 50 ft tall building casts a shadow that is 100 ft long. What is the angle of elevation of the sun above the horizon?

Accepted Answer

The angle is $$\arctan\left(\frac{50}{100}\right) = 26.6^\circ$$

Question 2

Given vector $$A = (28	ext{ ft}, 48^\circ)$$ and vector $$B = (28	ext{ m}, 18^\circ)$$, which of the following is the correct first step to add $$A$$ and $$B$$?

Accepted Answer

Convert $$B$$ from meters to feet before adding.

Question 3

After converting $$B to $$feet ($$1	ext{ m} = 3.281	ext{ ft}$$), what is the magnitude of $$B in $$feet?

Accepted Answer

$$28 	imes 3.281 = 91.868	ext{ ft}$$

Question 4

If you drive east at $$30	ext{ mph}$$ for $$2$$ hours and then north at $$30	ext{ m/s}$$ for another $$2$$ hours, what is your total displacement from the starting point? (Use $$1	ext{ mph} = 0.447	ext{ m/s})$$

Accepted Answer

Total displacement is $$\sqrt{(96,600	ext{ m})^2$ + (216,000	ext{ m})^2$}$$

Question 5

You start from rest and accelerate from $$30	ext{ mph} to$$ $$30	ext{ m/s} in$$ $$1$$ minute. What is your acceleration in $$	ext{m/s}^2$$? ($$1	ext{ mph} = 0.447	ext{ m/s})$$

Accepted Answer

$$a = \frac{30	ext{ m/s} - 13.41	ext{ m/s}}{60	ext{ s}} = 0.2765	ext{ m/s}^2$$

Question 6

A projectile is launched at $$23	ext{ m/s} at an $$angle of $$72^\circ. $$What is the vertical component of its initial velocity?

Accepted Answer

$$v_{0y} = 23 	imes \sin(72^\circ) = 21.85	ext{ m/s}$$

Question 7

For the projectile launched at $$23	ext{ m/s} at$$ $$72^\circ$$, what is the maximum height $$y_{max}$$ reached? (Use $$g = 9.8	ext{ m/s}^2)$$

Accepted Answer

$$y_{max} = \frac{(21.85)^2$}{2 	imes 9.8} = 24.34	ext{ m}$$

Question 8

What is the total time of flight $$t_f$$ for the projectile launched at $$23	ext{ m/s} at$$ $$72^\circ$$?

Accepted Answer

$$t_f = \frac{2 	imes 21.85}{9.8} = 4.46	ext{ s}$$

Question 9

What is the horizontal range $$\Delta x$$ for the projectile launched at $$23	ext{ m/s} at$$ $$72^\circ$$?

Accepted Answer

$$\Delta x = 7.12 	imes 4.46 = 31.77	ext{ m}$$

Question 10

If a vector $$A$$ has magnitude $$28	ext{ ft}$$ and direction $$48^\circ$$, what are its $$x$$ and $$y$$ components?

Accepted Answer

$$A_x = 28 	imes \cos(48^\circ) = 18.75	ext{ ft}$$, $$A_y = 28 	imes \sin(48^\circ) = 20.81	ext{ ft}$$

Question 11

A car travels east at $$30	ext{ mph}$$ for $$2$$ hours. How far does it travel in meters? ($$1	ext{ mi} = 1609	ext{ m})$$

Accepted Answer

$$60 	ext{ mi} 	imes 1609 = 96,540	ext{ m}$$

Question 12

If you drive north at $$30	ext{ m/s}$$ for $$2$$ hours, what is your displacement in meters?

Accepted Answer

$$30 	ext{ m/s} 	imes 7200 	ext{ s} = 216,000 	ext{ m}$$

Question 13

A projectile is launched at $$23	ext{ m/s} at$$ $$72^\circ. $$Which equation gives the time to reach maximum height?

Accepted Answer

$$t_{max} = \frac{v_{0y}}{g}$$

Question 14

If a vector $$B$$ has magnitude $$91.868	ext{ ft}$$ and direction $$18^\circ$$, what is its $$x$$ component?

Accepted Answer

$$B_x = 91.868 	imes \cos(18^\circ) = 87.41	ext{ ft}$$

Question 15

A projectile is launched at $$23	ext{ m/s} at$$ $$72^\circ. $$What is the formula for its horizontal range $$\Delta x$$?

Accepted Answer

$$\Delta x = v_{0x} 	imes t_f$$

Question 16

If you add vectors $$A$$ and $$B$$ after converting units, which method should you use?

Accepted Answer

Add their $$x$$ and $$y$$ components separately.

Question 17

A projectile is launched at $$23	ext{ m/s} at$$ $$72^\circ. $$What is the horizontal component of its initial velocity?

Accepted Answer

$$v_{0x} = 23 	imes \cos(72^\circ) = 7.12	ext{ m/s}$$

Physics Study Guide: Vectors, Kinematics, and Projectile Motion

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