Q: A car drives up a $$10^\circ$$ slope at $$15\ \mathrm{m/s}$$ for $$10 s. $$How much height does it gain?

$$\Delta y = v \sin \theta \cdot t = 15 \sin 10^\circ \times 10 = 26 m$$

Q: A skydiver falls vertically at $$35\ \mathrm{m/s}$$ while a wind blows at $$7\ \mathrm{m/s} to $$the west. What is the angle of his path with respect to vertical?

$$\theta = \tan$$^{-1}$$\left(\frac{7}{35}\right)$$

Q: A dog runs off a dock $$0.61 m $$above water at $$8.5 m/s. $$How far from the dock does it land?

$$x = v_x \Delta t = 8.5 \times 0.35 = 3.0 m$$

Question 1

Which of the following statements best describes a vector?

Accepted Answer

A quantity with both magnitude and direction.

Question 2

A hiker walks 4 km east and then 3 km north. What is the magnitude of the hiker's net displacement?

Accepted Answer

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

Question 3

If a vector $$\vec{A} is $$multiplied by a negative scalar $$-2$$, what happens to the resulting vector?

Accepted Answer

Its magnitude is doubled and its direction is reversed.

Question 4

Given $$\vec{A} = 5$$ units at $$30^\circ$$ above the x-axis, what are its x- and y-components?

Accepted Answer

$$A_x = 5 \cos 30^\circ$$, $$A_y = 5 \sin 30^\circ$$

Question 5

A car drives up a $$10^\circ$$ slope at $$15\ \mathrm{m/s}$$ for $$10 s. $$How much height does it gain?

Accepted Answer

$$\Delta y = v \sin 	heta \cdot t = 15 \sin 10^\circ 	imes 10 = 26 m$$

Question 6

A crate slides down a frictionless ramp inclined at $$30^\circ. $$What is the acceleration parallel to the ramp?

Accepted Answer

$$a_x = g \sin 30^\circ$$

Question 7

A projectile is launched with initial speed $$v_0 at $$angle $$	heta$$ above the horizontal. What is the initial vertical velocity component?

Accepted Answer

$$v_{y0} = v_0$ \sin 	heta$$

Question 8

A ball is dropped from rest and another is thrown horizontally from the same height at the same time. Neglecting air resistance, which hits the ground first?

Accepted Answer

They hit at the same time.

Question 9

A football is kicked at $$20\ \mathrm{m/s} at$$ $$37^\circ$$ above the horizontal. What is the time to reach maximum height?

Accepted Answer

$$t = \frac{v_0$ \sin 37^\circ}{g}$$

Question 10

A car moves around a circular track of radius $$r at $$constant speed $$v. $$What is the direction of its acceleration?

Accepted Answer

Toward the center of the circle.

Question 11

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

Accepted Answer

It increases by a factor of 4.

Question 12

A mouse runs across a conveyor belt moving at $$3\ \mathrm{m/s}$$ while the mouse runs at $$4\ \mathrm{m/s}$$ perpendicular to the belt. What is the mouse’s speed relative to the floor?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5 m/s$$

Question 13

A plane flies due east at $$500$$ mph. The wind blows due south at $$100$$ mph. What is the plane’s speed relative to the ground?

Accepted Answer

$$\sqrt{500^2$ + 100^2$} = 510$$ mph

Question 14

A skydiver falls vertically at $$35\ \mathrm{m/s}$$ while a wind blows at $$7\ \mathrm{m/s} to $$the west. What is the angle of his path with respect to vertical?

Accepted Answer

$$	heta = 	an$$^{-1}$$\left(\frac{7}{35}ight)$$

Question 15

Which of the following is true about projectile motion (neglecting air resistance)?

Accepted Answer

The horizontal and vertical motions are independent.

Question 16

A vector has components $$A_x = -3$$ and $$A_y = 4. $$What is its magnitude?

Accepted Answer

$$\sqrt{(-3)^2$ + 4^2$} = 5$$

Question 17

A dog runs off a dock $$0.61 m $$above water at $$8.5 m/s. $$How far from the dock does it land?

Accepted Answer

$$x = v_x \Delta t = 8.5 	imes 0.35 = 3.0 m$$

Ch 3 Vectors and Motion in Two Dimensions: Study Notes

Guida di studio - Domande di pratica

Study guide - Flashcard