Q: Which of the following is the correct formula for the range $$R of a $$projectile launched from ground level at speed $$v_0$$ and angle $$\theta$$ above the horizontal (neglecting air resistance)?

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

Q: A projectile is launched at $$v_0 at an $$angle $$\theta$$ above the horizontal. Which of the following correctly gives the vertical component of its velocity at time $$t$$?

$$v_{y} = v_0$ \sin \theta - g t$$

Question 1

A soccer ball is kicked from the ground with an initial speed 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? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$5.1\ \mathrm{m}$$

Question 2

Which of the following best describes the direction of the instantaneous velocity vector for a particle moving along a curved path in the $$x$$-$$y$$ plane?

Accepted Answer

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

Question 3

A projectile is launched horizontally from the top of a $$45\ \mathrm{m}$$ high cliff with a speed of $$15\ \mathrm{m/s}. $$How far from the base of the cliff does the projectile land? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$30.6\ \mathrm{m}$$

Question 4

Which equation correctly gives the $$x-$$component of the initial velocity for a projectile launched at speed $$v_0$$ and angle $$	heta$$ above the horizontal?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$

Question 5

A car moves from point $$A at$$ $$(2, 3) to $$point $$B at$$ $$(8, 11) in$$ $$4$$ seconds. What is the magnitude of its average velocity?

Accepted Answer

$$2.0\sqrt{5}\ \mathrm{m/s}$$

Question 6

Which of the following statements about projectile motion (neglecting air resistance) is correct?

Accepted Answer

The horizontal acceleration is zero and the vertical acceleration is $$-g.$$

Question 7

A baseball is hit with an initial velocity of $$40\ \mathrm{m/s} at an $$angle of $$37^\circ$$ above the horizontal. What is the time of flight until it returns to the same vertical level? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$4.8\ \mathrm{s}$$

Question 8

A carnival ride moves in a circle of radius $$10\ \mathrm{m} at a $$constant speed of $$8\ \mathrm{m/s}. $$What is the magnitude of the centripetal acceleration?

Accepted Answer

$$6.4\ \mathrm{m/s^2$}$$

Question 9

A boat heads due east across a river at $$5\ \mathrm{m/s}$$ relative to the water. The river flows due north at $$3\ \mathrm{m/s}. $$What is the boat's speed relative to the ground?

Accepted Answer

$$5.83\ \mathrm{m/s}$$

Question 10

Which of the following is the correct formula for the range $$R of a $$projectile launched from ground level at speed $$v_0$$ and angle $$	heta$$ above the horizontal (neglecting air resistance)?

Accepted Answer

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

Question 11

A cyclist travels $$12\ \mathrm{km}$$ east, then $$5\ \mathrm{km}$$ north. What is the magnitude of the displacement from the starting point?

Accepted Answer

$$13\ \mathrm{km}$$

Question 12

A model car moves from $$(0,0) to$$ $$(3,4) in$$ $$2$$ seconds. What is the direction of its average velocity vector with respect to the $$x-$$axis?

Accepted Answer

$$53.1^\circ$$

Question 13

A projectile is launched at $$v_0 at an $$angle $$	heta$$ above the horizontal. Which of the following correctly gives the vertical component of its velocity at time $$t$$?

Accepted Answer

$$v_{y} = v_0$ \sin 	heta - g t$$

Question 14

A plane flies with an airspeed of $$200\ \mathrm{km/h}$$ due north, but there is a wind blowing $$50\ \mathrm{km/h}$$ due east. What is the plane's velocity relative to the ground?

Accepted Answer

$$\sqrt{200^2$ + 50^2$}\ \mathrm{km/h} at$$ $$14.0^\circ$$ east of north

Question 15

Which of the following is true about the acceleration of a particle in uniform circular motion?

Accepted Answer

It is always directed toward the center of the circle.

Question 16

A football is kicked at $$25\ \mathrm{m/s} at an $$angle of $$45^\circ$$ above the horizontal. What is the total time the ball spends in the air? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.6\ \mathrm{s}$$

Question 17

A car rounds a curve of radius $$50\ \mathrm{m} at a $$constant speed of $$20\ \mathrm{m/s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$8.0\ \mathrm{m/s^2$}$$

Question 18

A projectile is launched from the ground at $$v_0$$ and angle $$	heta. At $$the highest point of its trajectory, which of the following is true?

Accepted Answer

The vertical component of velocity is zero.

Question 19

A ball is thrown with a velocity of $$10\ \mathrm{m/s} at$$ $$60^\circ$$ above the horizontal. What is the horizontal distance traveled before it lands? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$8.84\ \mathrm{m}$$

Motion in a Plane: Position, Velocity, Acceleration, and Projectile Motion

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