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 height?

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

Q: A projectile is launched at $$v_0$$ and angle $$\theta. $$What is the maximum range (on level ground) if air resistance is neglected?

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

Question 1

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

Accepted Answer

$$10\ \mathrm{m/s}$$

Question 2

Which of the following is always a positive quantity for a vector?

Accepted Answer

Magnitude

Question 3

A car drives up a $$10^\circ$$ slope at a constant speed of $$15\ \mathrm{m/s}. $$How much height does the car gain after $$10\ \mathrm{s}$$?

Accepted Answer

$$26\ \mathrm{m}$$

Question 4

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

Accepted Answer

$$a = g \sin	heta$$

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 height?

Accepted Answer

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

Question 6

A 100-g ball rolls off a table and lands $$2.0\ \mathrm{m}$$ from the base. A 200-g ball rolls off the same table with the same speed. Where does it land?

Accepted Answer

$$2.0\ \mathrm{m}$$

Question 7

A car is traveling around a curve at a steady $$45\ \mathrm{mph}. Is $$the car accelerating?

Accepted Answer

Yes

Question 8

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

Accepted Answer

$$4$$

Question 9

A mouse runs straight across a conveyor belt moving at $$3\ \mathrm{m/s}$$, heading for cheese at $$4\ \mathrm{m/s} ($$relative to the belt). What is the mouse’s speed relative to the factory floor?

Accepted Answer

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

Question 10

A plane flies due east at $$500\ \mathrm{mph}$$ relative to the air. The 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 11

A projectile is launched at $$v_0$$ and angle $$	heta. $$What is the maximum range (on level ground) if air resistance is neglected?

Accepted Answer

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

Question 12

Which statement about projectile motion is correct (neglecting air resistance)?

Accepted Answer

The horizontal and vertical motions are independent.

Question 13

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

Accepted Answer

$$5$$

Question 14

A speed skater moves at $$11.1\ \mathrm{m/s}$$ around a turn of radius $$11\ \mathrm{m}. $$What is the magnitude of her centripetal acceleration?

Accepted Answer

$$11.2\ \mathrm{m/s^2$}$$

Question 15

A projectile is launched and lands at the same height. Which launch angle gives the maximum range?

Accepted Answer

$$45^\circ$$

Question 16

A ball is thrown horizontally from a $$20\ \mathrm{m}$$ high cliff with a speed of $$5\ \mathrm{m/s}. $$How long does it take to hit the ground? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.02\ \mathrm{s}$$

Question 17

A vector $$\vec{A}$$ has a magnitude of $$6.0\ \mathrm{m/s^2$}$$ and points $$30^\circ$$ below the negative x-axis. What are its x- and y-components?

Accepted Answer

$$-5.2, -3.0$$

Question 18

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

Accepted Answer

$$11.3^\circ$$

Question 19

Which of the following best describes the acceleration vector for an object in uniform circular motion?

Accepted Answer

It points toward the center of the circle.

Vectors and Motion in Two Dimensions: Physics with Calculus Study Notes

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