1. Wilhem Tell, legendary archer and hero of Swiss independence, was forced to shoot at an Apple palced on his son´s head. If Tell must stand 13 m from his son and he launches the arrow with a speed of vi = 58 m/s, at what angle θi above the horizontal should he point the arrow? Assume the arrow starts at the same height as tha Apple and neglect air resistance.
2.A monkey is hanging from a branch in a tree 3 m
away from a zookeeper and 2 m above the keeper´s hand (figure). The keeper knows that the monkey always lets
go of the branch just as the banana is thrown to it. At what angle must the keeper throw the
banana for the monkey to catch it?.
3. If the monkey of the exemple, stay in the tree on a branch 2 m. high, at
what angle must the zookeeper throw the banana (at 8 m/s) for it to reach the
monkey 3 m away.
4. The skier leaves the snow with velocity 11 m/s,
23° below the horizontal, and lands on 55° slope below. (figure).
Where and when does the land? What
is her velocity when she hits the snow?.
5. In the movie, the god must be crazy, a bottle
is thrown from a cliff overlooking the
Indian Ocean. If the cliff is 0,5 km
high, and the bottle is thrown
horizontally at an initial speed of 10 m/s what are the bottle position and
velocity 0,5 s later?. Neglecting
effects of air resistance, find the distance from the bottom of the cliff at
which the bottle hits the water. Find its
velocity just before impact.
6. In a circus act, clowns are shot from a cannon
at a constant speed vo = 10.4
m/s. The angle of launch may be
varied. What is the maximum distance D
that a clown may travel, if the landing pad is at the same height as the mouth
of the cannon?. The circus master wants
to shoot two clowns from his cannon, one after the other, and have them land on
the same landing pad a distance D/2 away at the same time. How can it be done? How long should be he
wait to lunch the second clown?.
7. A tennis
player standing 12 m from a net high
hits a ball so as just to land inside the back line, 12 m beyond the net. The initial height of the ball is 0,5 m. Find the initial velocity and angle required
for the ball just to clear the net.
8. On
the moon, mail may be sent in cannister launched by mass drivers. The settlement of Rimtown and Crater City are
separated by steep cliff. The Rimtown mass driver has a constant launch
speed vi and a maximum range , where D is the horizontal distance to the
cliff edge. (Range here still means the horizontal distance a projectile would
go between points at the same height).
What is the launch speed from the Rimtown mass driver? At what minimum distance d from the cliff can the postmaster of Crater City locate the
reception point for mail from Rimtown?.
