Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the time of flight if it lands at the same height from which it was launched? (Neglect air resistance.)

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

Q: A grasshopper jumps a distance $$d at $$the optimal angle for maximum range. What is the initial speed $$v_0$$ required? (Assume $$g is $$the acceleration due to gravity.)

$$v_0$$ = \sqrt{g d}$$ at $$\theta = 45^\circ$$

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° slope at a constant speed of $$15\ \mathrm{m/s}$$ for $$10\ \mathrm{s}. $$How much height does the car gain? (Use $$\sin 10° \approx 0.174)$$

Accepted Answer

$$26\ \mathrm{m}$$

Question 4

A crate slides down a frictionless ramp inclined 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 horizontal component of its initial velocity?

Accepted Answer

$$v_0$$ \cos 	heta$$

Question 6

A 100-g ball and a 200-g ball roll off the same table with the same speed. The 100-g ball lands 2.0 m from the base. Where does the 200-g ball land?

Accepted Answer

2.0 m

Question 7

A car travels around a circular track at constant speed. Which statement is true about its acceleration?

Accepted Answer

It points toward the center of the circle.

Question 8

A toy car moves around a circular track at constant speed. If the car doubles its speed, by what factor does the 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 factory floor?

Accepted Answer

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

Question 10

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 11

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the time of flight if it lands at the same height from which it was launched? (Neglect air resistance.)

Accepted Answer

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

Question 12

A skydiver falls at $$35\ \mathrm{m/s}$$ vertically while a wind blows at $$7\ \mathrm{m/s} to $$the west. What is the magnitude of the skydiver's velocity relative to the ground?

Accepted Answer

$$\sqrt{35^2$ + 7^2$}\ \mathrm{m/s}$$

Question 13

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

Accepted Answer

$$5$$

Question 14

A projectile is launched horizontally from a height $$h$$ with speed $$v_0. $$What is the time it takes to hit the ground?

Accepted Answer

$$\sqrt{\dfrac{2h}{g}}$$

Question 15

A vector $$\vec{A} is $$multiplied by $$-1. $$What happens to the vector?

Accepted Answer

Its direction reverses, magnitude unchanged.

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

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

Question 17

Which of the following best describes the acceleration vector for a particle in projectile motion (neglecting air resistance)?

Accepted Answer

It is directed downward at all times.

Question 18

A grasshopper jumps a distance $$d at $$the optimal angle for maximum range. What is the initial speed $$v_0$$ required? (Assume $$g is $$the acceleration due to gravity.)

Accepted Answer

$$v_0$$ = \sqrt{g d}$$ at $$	heta = 45^\circ$$

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

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