Q: A car drives up a slope at a constant speed of $$15\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. If $$the slope makes an angle $$\theta$$ with the horizontal, what is the vertical height gained by the car?

$$15 \times 10 \times \sin\theta$$

Q: A projectile is launched with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the time of flight until it lands at the same vertical level?

$$\dfrac{2 v_0$ \sin\theta}{g}$$

Q: A ball is thrown horizontally from a $$2.0\ \mathrm{m}$$ high table with a speed of $$3.0\ \mathrm{m/s}. $$How long does it take to hit the ground? (Neglect air resistance.)

$$\sqrt{\dfrac{2 \times 2.0}{9.8}}$$

Q: A projectile is launched at speed $$v_0$$ and angle $$\theta$$ above the horizontal. What is the maximum range (horizontal distance) it can achieve on level ground (neglecting air resistance)?

$$\dfrac{v_0$^2 \sin 2\theta}{g}$$

Q: A dog runs horizontally off a dock $$0.61\ \mathrm{m}$$ above the water at $$8.5\ \mathrm{m/s}. $$How far from the dock does the dog land? (Neglect air resistance.)

$$8.5 \times \sqrt{\dfrac{2 \times 0.61}{9.8}}$$

Question 1

A soccer ball is kicked straight up and takes 2.0 s to reach its highest point. What was its initial velocity? (Assume $$g = 9.8\ \mathrm{m/s^2$}$$ downward.)

Accepted Answer

$$20\ \mathrm{m/s}$$

Question 2

Which of the following statements about vectors is correct?

Accepted Answer

The magnitude of a vector is always a positive quantity.

Question 3

A car drives up a slope at a constant speed of $$15\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. If $$the slope makes an angle $$	heta$$ with the horizontal, what is the vertical height gained by the car?

Accepted Answer

$$15 	imes 10 	imes \sin	heta$$

Question 4

A crate slides down a frictionless ramp tilted at angle $$	heta. $$What is the acceleration of the crate parallel to the ramp?

Accepted Answer

$$g \sin	heta$$

Question 5

A projectile is launched with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the time of flight until it lands at the same vertical level?

Accepted Answer

$$\dfrac{2 v_0$ \sin	heta}{g}$$

Question 6

A ball is thrown horizontally from a $$2.0\ \mathrm{m}$$ high table with a speed of $$3.0\ \mathrm{m/s}. $$How long does it take to hit the ground? (Neglect air resistance.)

Accepted Answer

$$\sqrt{\dfrac{2 	imes 2.0}{9.8}}$$

Question 7

A car travels 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 8

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

Accepted Answer

4

Question 9

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

Accepted Answer

$$5\ \mathrm{m/s}$$

Question 10

A projectile is launched at speed $$v_0$$ and angle $$	heta$$ above the horizontal. What is the maximum range (horizontal distance) it can achieve on level ground (neglecting air resistance)?

Accepted Answer

$$\dfrac{v_0$^2 \sin 2	heta}{g}$$

Question 11

A plane flies due east at $$500\ \mathrm{mph}$$ while a wind blows due south at $$100\ \mathrm{mph}. $$What is the plane’s speed relative to the ground?

Accepted Answer

$$\sqrt{500^2$ + 100^2$}\ \mathrm{mph}$$

Question 12

A dog runs horizontally off a dock $$0.61\ \mathrm{m}$$ above the water at $$8.5\ \mathrm{m/s}. $$How far from the dock does the dog land? (Neglect air resistance.)

Accepted Answer

$$8.5 	imes \sqrt{\dfrac{2 	imes 0.61}{9.8}}$$

Question 13

Which of the following best describes the acceleration of a projectile in flight (neglecting air resistance)?

Accepted Answer

It is always directed downward with magnitude $$g.$$

Question 14

A skydiver falls at $$35\ \mathrm{m/s}$$ vertically 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

$$\arctan\left(\dfrac{7}{35}\right)$$ west of vertical

Question 15

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

Accepted Answer

$$5$$

Question 16

A car rounds a curve of radius $$25\ \mathrm{m} on $$wet pavement. If the maximum advisable acceleration is $$0.40g$$, what is the maximum speed the car should have?

Accepted Answer

$$\sqrt{0.40g 	imes 25}$$

Question 17

Which of the following is true about the horizontal and vertical motions of a projectile?

Accepted Answer

They are independent of each other.

Chapter 3: Vectors and Motion in Two Dimensions – Study Notes

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