Q: A projectile is launched from ground level with initial speed $$v_0 at an $$angle $$\theta$$ above the horizontal. Neglecting air resistance, what is the time of flight until it lands back on the ground?

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

Q: A projectile is launched horizontally from a $$5\ \mathrm{m}$$ high platform with an initial speed of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is the speed with which it hits the ground?

$$\sqrt{10^2$ + (2g \times 5)}\ \mathrm{m/s}$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$What is the maximum range (on level ground) achieved, and at what angle does it occur?

Maximum range at $$\theta = 45^\circ$$

Question 1

A car moves from the point $$(2.0\ \mathrm{m},\ 1.0\ \mathrm{m}) to$$ $$(3.0\ \mathrm{m},\ 5.0\ \mathrm{m}) in$$ $$4.0\ \mathrm{s}. $$What is the average velocity vector of the car?

Accepted Answer

$$\left(0.25\ \mathrm{m/s},\ 1.0\ \mathrm{m/s}\right)$$

Question 2

A racing driver completes 60 laps of a $$5\ \mathrm{km}$$ circuit, starting and finishing $$30\ \mathrm{m}$$ apart along the finish line. What is the driver's total displacement vector?

Accepted Answer

$$\left(0\ \mathrm{m},\ 30\ \mathrm{m}\right)$$

Question 3

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

Accepted Answer

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

Question 4

A car is moving along a circular path at constant speed. What is the direction of its acceleration vector?

Accepted Answer

Toward the center of the circle

Question 5

For a particle moving in a circle of radius $$R at $$constant speed $$v$$, what is the magnitude of its acceleration?

Accepted Answer

$$a = \frac{v^2$}{R}$$

Question 6

A projectile is launched from ground level with initial speed $$v_0 at an $$angle $$	heta$$ above the horizontal. Neglecting air resistance, what is the time of flight until it lands back on the ground?

Accepted Answer

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

Question 7

A golf ball is hit on the Moon with the same initial speed and angle as on Earth. The acceleration due to gravity on the Moon is $$1/6$$ that on Earth. How does the range of the ball on the Moon compare to that on Earth?

Accepted Answer

It will be 6 times larger

Question 8

A monkey runs at $$4.0\ \mathrm{m/s} on a $$crocodile's back, which is drifting at $$3.0\ \mathrm{m/s}$$ relative to the shore. What is the monkey's speed relative to the shore if it runs in the same direction as the crocodile's motion?

Accepted Answer

$$7.0\ \mathrm{m/s}$$

Question 9

A projectile is launched horizontally from a $$5\ \mathrm{m}$$ high platform with an initial speed of $$10\ \mathrm{m/s}. $$Neglecting air resistance, what is the speed with which it hits the ground?

Accepted Answer

$$\sqrt{10^2$ + (2g 	imes 5)}\ \mathrm{m/s}$$

Question 10

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

Accepted Answer

The horizontal velocity remains constant while the vertical velocity changes due to gravity.

Question 11

A car moves around a circular track at $$30\ \mathrm{mph}. If $$the speed is doubled to $$60\ \mathrm{mph}$$, how does the magnitude of the centripetal acceleration change?

Accepted Answer

It becomes four times larger

Question 12

A swimmer wants to cross a river flowing east at $$2\ \mathrm{m/s}. $$The swimmer can swim at $$3\ \mathrm{m/s}$$ relative to the water. To reach a point directly north on the opposite bank, in which direction should the swimmer head?

Accepted Answer

Northwest, at an angle $$\arccos\left(\frac{2}{3}\right)$$ west of north

Question 13

Which of the following is true about the acceleration vector for a particle moving along a curved path at constant speed?

Accepted Answer

It is perpendicular to the velocity vector.

Question 14

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$What is the maximum range (on level ground) achieved, and at what angle does it occur?

Accepted Answer

Maximum range at $$	heta = 45^\circ$$

Question 15

Which of the following best describes the effect of air resistance on a projectile's trajectory?

Accepted Answer

The maximum height and range both decrease, and the trajectory is no longer a parabola.

Question 16

A person walks at $$1.0\ \mathrm{m/s} on a $$train moving at $$10.0\ \mathrm{m/s}$$ 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

$$11.0\ \mathrm{m/s}$$

Question 17

A particle moves in a circle of radius $$R$$ with speed $$v$$ that is increasing at a constant rate $$a_t. $$What is the magnitude of the total acceleration?

Accepted Answer

$$a = \sqrt{a_t^2$ + \left(\frac{v^2$}{R}\$$right)^2$$}$$

Motion in Two Dimensions: Vectors, Acceleration, and Projectile Motion

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