Q: A projectile is launched with an initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. What is the formula for the range $$R of $$the projectile (neglecting air resistance)?

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

Question 1

A soccer ball is kicked from the ground with an initial velocity of $$20\ \mathrm{m/s} at an $$angle of $$30^\circ$$ above the horizontal. Neglecting air resistance, what is the maximum height reached by the ball? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$5.1\ \mathrm{m}$$

Question 2

Which of the following statements about projectile motion is correct?

Accepted Answer

The horizontal and vertical motions are independent except for sharing the same time of flight.

Question 3

A ball is thrown horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How far from the base of the cliff does the ball land? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$30.3\ \mathrm{m}$$

Question 4

Given a velocity vector $$\vec{v}$$ with components $$v_x = 6\ \mathrm{m/s}$$ and $$v_y = 8\ \mathrm{m/s}$$, what is the magnitude of $$\vec{v}$$?

Accepted Answer

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

Question 5

A model car moves from point $$P_1 at$$ $$(2.0\ \mathrm{s},\ 4.0\ \mathrm{m},\ 2.0\ \mathrm{m}) to $$point $$P_2 at$$ $$(2.5\ \mathrm{s},\ 7.0\ \mathrm{m},\ 6.0\ \mathrm{m}). $$What is the $$y-$$component of the average velocity?

Accepted Answer

$$8.0\ \mathrm{m/s}$$

Question 6

Which of the following best describes the instantaneous velocity vector of a particle moving along a curved path?

Accepted Answer

It is always tangent to the path at the particle's position.

Question 7

A projectile is launched with an initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the formula for the range $$R of $$the projectile (neglecting air resistance)?

Accepted Answer

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

Question 8

A baseball is hit at ground level with a speed of $$40\ \mathrm{m/s} at an $$angle of $$45^\circ. $$What is the total time the ball spends in the air? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$5.8\ \mathrm{s}$$

Question 9

Which of the following is true about the acceleration of a projectile in flight (neglecting air resistance)?

Accepted Answer

The acceleration is constant and directed downward.

Question 10

A boat moves east at $$5\ \mathrm{m/s}$$ relative to the water, while the river flows north at $$3\ \mathrm{m/s}. $$What is the boat's speed relative to an observer on the shore?

Accepted Answer

$$5.8\ \mathrm{m/s}$$

Question 11

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

Accepted Answer

$$v_0$$ \sin 	heta$$

Question 12

A football is kicked at $$25\ \mathrm{m/s} at an $$angle of $$37^\circ$$ above the horizontal. What is the horizontal component of its initial velocity?

Accepted Answer

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

Question 13

Which of the following best describes the process of vector addition using the head-to-tail method?

Accepted Answer

Place the tail of the second vector at the head of the first; the resultant is from the tail of the first to the head of the second.

Question 14

A projectile is launched at $$v_0$$ and angle $$	heta. At $$the peak of its trajectory, which statement is true?

Accepted Answer

The vertical component of velocity is zero.

Question 15

A car travels $$100\ \mathrm{m}$$ east, then $$100\ \mathrm{m}$$ north. What is the magnitude of its displacement from the starting point?

Accepted Answer

$$141\ \mathrm{m}$$

Question 16

If a vector $$\vec{A}$$ has components $$A_x = -3$$ and $$A_y = 4$$, what is the angle $$	heta it $$makes with the positive $$x-$$axis?

Accepted Answer

$$126.9^\circ$$

Question 17

Which of the following is a correct statement about average acceleration in two dimensions?

Accepted Answer

Average acceleration is the change in velocity vector divided by the time interval.

Question 18

A projectile is fired at $$60^\circ$$ above the horizontal with a speed of $$50\ \mathrm{m/s}. $$What is the time to reach the maximum height? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$4.4\ \mathrm{s}$$

Question 19

A rescue plane flying horizontally at $$60\ \mathrm{m/s}$$ drops a package from a height of $$180\ \mathrm{m}. $$Where does the package land relative to the point directly below where it was released? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$360\ \mathrm{m}$$

Motion in a Plane: Position, Velocity, and Acceleration in Two Dimensions

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