Physics homework #02

1. You throw a ball vertically upward from the roof of a tall building. The ball leaves your hand at a

point even with the roof railing with an upward speed v

0y

= 15.0 m/s; the ball is then in free fall.

On its way back down, it just misses the railing. At the location of the building, g = 9.80 m/s

2

.

Find (a) the position and velocity of the ball 1.0 s and 4.0 s after leaving your hand; (b) the velocity
when the ball is 5.0 m above the railing; (c) the maximum height reached and the time at which it
is reached; and (d) the acceleration of the ball when it is at its maximum height, (e) the time when
the ball is 5.0 m below the roof railing. (f) Draw the y-t and v

y

-t graphs.

2. A marble is released from one rim of a hemispherical bowl of diameter 50.0 cm and rolls down and

up to the opposite rim in 10.0 s. Find (a) the average speed and (b) the average velocity of the
marble.

3. A ball is thrown straight up from the ground with speed v

0

. At the same instant, a second ball is

dropped from rest from a height H, directly above the point where the first ball was thrown upward.
There is no air resistance. (a) Find the time at which the two balls collide. (b) Find the value of
H in terms of v

0

and g so that at the instant when the balls collide, the first ball is at the highest

point of its motion.

4. An alert hiker sees a boulder fall from the top of a distant cliff and notes that it takes 1.30 s for the

boulder to fall the last third of the way to the ground. You may ignore air resistance. (a) What is
the height of the cliff in meters? (b) If in part (a) you get two solutions of a quadratic equation and
you use one for your answer, what does the other solution represent?

5. A motorcycle stunt rider rides off the edge of a cliff. Just at the edge his velocity is horizontal, with

magnitude 9.0 m/s. Find the motorcycle’s position, distance from the edge of the cliff, and velocity
after 0.50 s.

6. For a projectile launched with speed v

0

at initial angle α

0

(between 0 and π/2), derive general

expression for the maximum height h and horizontal range R. For a given v

0

, what value of α

0

gives

maximum height? What value gives maximum horizontal range?

7. A monkey escapes from the zoo and climbs a tree. After failing to entice the monkey down, the zoo

keeper standing on the ground fires a tranquillizer dart directly at the monkey. The clever monkey
lets go at the same instant the dart leaves the gun barrel, intending to land on the ground and escape.
Show that the dart always hits the monkey, regardless of the dart’s muzzle velocity (provided that
it gets to the monkey before he hits the ground).

8. The earth has a radius of 6380 km and turns around once on its axis in 24 h. (a) What is the radial

acceleration of an object at the earth’s equator? Give your answer in m/s

2

and as a fraction of g.

(b) If a

rad

at the equator is greater than g, object would fly off the earth’s surface and into space.

What would the period of the earth’s rotation have to be for this to occur?

9. For no apparent reason, a poodle is running at a constant speed of v = 5.0 m/s in a circle with

radius R = 2.5 m. Let

−

→

v

1

be the velocity vector at time t

1

, and let

−

→

v

2

be the velocity vector at

time t

2

. Consider ∆

−

→

v =

−

→

v

2

− −

→

v

1

and ∆t = t

2

− t

1

. For ∆t = 0.5 s, 0.1 s, and 0.05 s, calculate the

magnitude (to four significant figures) and direction (relative to

−

→

v

1

) of the average acceleration

−→

a

av

.

Compare your results to the general expression for the instantaneous acceleration

−

→

a for uniform

circular motion.

Maciej Wo loszyn

WFiIS AGH

http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/