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

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

Question 1

A projectile is fired at an angle $$	heta$$ above the horizontal with an initial speed $$v_0. $$Which of the following statements about its motion is NOT true?

Accepted Answer

The component of the velocity is zero at the highest point of the trajectory.

Question 2

A $$3.0\ \mathrm{kg}$$ projectile is fired into the air from the ground and lands back at the same height. If its initial vertical velocity is $$7.8\ \mathrm{m/s}$$, what is the speed of the projectile just before it hits the ground? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$7.8\ \mathrm{m/s}$$

Question 3

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

Accepted Answer

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

Question 4

A projectile is at the apex of its trajectory when a wind gust with a horizontal speed $$v_w$$ suddenly acts on it. What is the most likely effect of the wind on the projectile's motion?

Accepted Answer

The projectile's horizontal range will increase because the wind adds to the horizontal velocity.

Question 5

A child sleds down a snowy hill. In Case 1, the child sits upright; in Case 2, the child lies flat on the sled. Which case will experience more friction force and why?

Accepted Answer

Case 1, because the vertical component of applied force is increasing, increasing the normal force and thus the friction force.

Question 6

A force $$F$$ acts on a mass $$m$$ for a time interval $$\Delta t$$, changing its velocity from $$v_0 to$$ $$v_f. $$What is the average force exerted during this interval?

Accepted Answer

$$F_{\mathrm{avg}} = m \dfrac{v_f - v_0$}{\Delta t}$$

Question 7

A $$20\ \mathrm{N}$$ bucket is at the bottom of a $$9\ \mathrm{m}$$ deep well and is initially at rest. The bucket is then pulled to the top of the well by a string that exerts a constant tension force such that it reaches the top in $$10\ \mathrm{s}. $$What is the tension in the string?

Accepted Answer

$$24\ \mathrm{N}$$

Question 8

A block of mass $$m$$ rests on a table. You apply a small force to the block, but it does not move. Which of the following is an action-reaction pair according to Newton's third law?

Accepted Answer

The block's push on the table and the table's push on the block.

Question 9

A car is moving in a circle of radius $$r at $$constant speed $$v. $$Which force provides the centripetal acceleration that keeps the car in circular motion?

Accepted Answer

The friction force between the tires and the road.

Question 10

What is the maximum velocity that a car of mass $$m$$ can have in a turn of radius $$r$$ before it starts to skid, given the coefficient of static friction $$\mu_s$$ between the tires and the road? (Assume level ground.)

Accepted Answer

$$v = \sqrt{\mu_s g r}$$

Question 11

If a car is taking a turn on an icy road and the coefficient of static friction between the tires and the road drops to zero, what will happen to the motion of the car?

Accepted Answer

The car will slide off the road in a straight line due to the tendency of an object to maintain direction and magnitude of velocity (Newton's first law).

Question 12

Three asteroids, A, B, and C, are aligned in space. Asteroids B and C have the same mass $$M$$, while asteroid A has twice the mass $$2M. $$The distance between A and B is the same as between B and C. Which statement is correct about the gravitational field strengths at the positions of B and C due to A?

Accepted Answer

$$g_B = 2g_C$$

Question 13

A student claims: "Asteroid A will attract Asteroid B with more force than Asteroid B will attract Asteroid A because Asteroid A has a bigger mass than Asteroid B." Do you agree or disagree with this statement?

Accepted Answer

Disagree, because the force of attraction is equal in magnitude and opposite in direction according to Newton's third law.

Question 14

A car of mass $$m is $$moving at speed $$v on a $$flat road. The normal force from the road and the weight of the car are shown on a free-body diagram. What is the net vertical force acting on the car?

Accepted Answer

Zero, because the normal force balances the weight.

Question 15

A $$5\ \mathrm{kg}$$ object is pulled across a horizontal surface with a force of $$20\ \mathrm{N} at an $$angle of $$30^\circ$$ above the horizontal. If the coefficient of kinetic friction is $$0.2$$, what is the acceleration of the object? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$2.1\ \mathrm{m/s^2$}$$

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