Question 1

Which of the following best describes a vector quantity?

Accepted Answer

A quantity that has both magnitude and direction.

Question 2

A car travels 8 km east, then 6 km west. What is the resultant displacement?

Accepted Answer

$$2\ 	ext{km}$$ east

Question 3

A hiker walks 4.00 m north and then 2.00 m west. What is the magnitude of the net displacement?

Accepted Answer

$$4.47\ 	ext{m}$$

Question 4

Which of the following is a scalar quantity?

Accepted Answer

Mass

Question 5

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

Accepted Answer

It has twice the magnitude and points in the opposite direction as $$\vec{V}.$$

Question 6

A projectile is launched horizontally from a cliff with an initial velocity $$v_{x0}. $$Which of the following statements is true about its motion?

Accepted Answer

The horizontal velocity remains constant while the vertical velocity increases linearly with time.

Question 7

A football is kicked from the ground at an angle $$\$$theta_0$$ = 37^\circ$$ with a velocity of $$20.0\ 	ext{m/s}. $$What is the initial vertical component of the velocity?

Accepted Answer

$$v_{y0} = 20.0 \sin 37^\circ$$

Question 8

A boat wants to cross a river directly from south to north. The river flows east at $$5\ 	ext{m/s}$$, and the boat can move at $$14\ 	ext{m/s} in $$still water. At what angle west of north should the boat head?

Accepted Answer

$$\arcsin\left(\frac{5}{14}\right)$$

Question 9

A car drives off a cliff with a horizontal velocity of $$11.1\ 	ext{m/s}$$ and lands $$50\ 	ext{m}$$ from the base. How long is the car in the air?

Accepted Answer

$$4.50\ 	ext{s}$$

Question 10

Which equation gives the range $$R of a $$projectile launched at speed $$v_0$$ and angle $$\$$theta_0$$ from the ground (neglecting air resistance)?

Accepted Answer

$$R = \frac{v_0$^2 \sin 2\$$theta_0$$}{g}$$

Question 11

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

Accepted Answer

$$5$$

Question 12

Which of the following best describes the path of a projectile under the influence of gravity (neglecting air resistance)?

Accepted Answer

A parabola

Question 13

A ball is thrown with an initial velocity $$v_0 at an $$angle $$\$$theta_0$$ above the horizontal. At the highest point of its trajectory, which statement is true?

Accepted Answer

The vertical component of velocity is zero.

Question 14

A person walks at $$2\ 	ext{m/s}$$ inside a train moving at $$9\ 	ext{m/s}$$ relative to the ground. What is the person's speed relative to the ground if they walk in the same direction as the train?

Accepted Answer

$$11\ 	ext{m/s}$$

Question 15

A projectile is launched at $$45^\circ$$ with initial speed $$v_0. At $$what angle is the range maximized (neglecting air resistance)?

Accepted Answer

$$45^\circ$$

Question 16

If air resistance is considered, how does the range of a projectile compare to the ideal case (no air resistance)?

Accepted Answer

The range is less with air resistance.

Question 17

A vector $$\vec{V}$$ makes an angle $$	heta$$ with the x-axis. Which equation gives the y-component of $$\vec{V}$$?

Accepted Answer

$$V_y = V \sin 	heta$$

Question 18

A ball is thrown horizontally from a $$20\ 	ext{m}$$ high cliff with a speed of $$5\ 	ext{m/s}. $$How far from the base of the cliff does the ball land? (Take $$g = 9.8\ 	ext{m/s}^2)$$

Accepted Answer

$$10.1\ 	ext{m}$$

Question 19

Which of the following is the correct equation for the time of flight $$T of a $$projectile launched from the ground at speed $$v_0$$ and angle $$\$$theta_0$$?

Accepted Answer

$$T = \frac{2 v_0$ \sin \$$theta_0$$}{g}$$

Kinematics in Two Dimensions and Vectors – Study Notes

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