1. A ball is thrown horizontally from a cliff at a speed of 10 m/s. You predict that its speed I s later will be slightly greater than 14 m/s. Your friend says it will be 10 m/s. Show who is correct.
2. You're in an airplane that flies horizontally with speed 1000 km/h (280 m/s) when an engine falls off. Neglecting air resistance, assume it takes 30 s for the engine to hit the ground.
a. Show that the airplane is 4.5 km high.
b. Show that the horizontal distance that the aircraft engine falls is 8400 m.
c. If the airplane somehow continues to fly as if nothing had happened, where is the engine relative to the air-plane at the moment the engine hits the ground?
3. A cannonball shot with an initial velocity of 141 m/s at an angle of 45° follows a parabolic path and hits a balloon at the top of its trajectory. Neglecting air resistance, show that the cannonball hits the balloon at a speed of 100 m/s.
4. Students in Chuck Stone's lab measure the speed of a steel ball to be 8.0 m/s when launched horizon-tally from a 1.0-m high tabletop. Their objective is to place a 20-cm tall coffee can on the floor to catch the ball. Show that they score a bull's-eye when the can is placed 3.2 m from the base of the table.
5. At a particular point in orbit a satellite in an elliptical orbit has a gravitational potential energy of 5000 MJ with respect to Earth's surface and a kinetic energy of 4500 MJ. Later in its orbit, the satellite's potential energy is 6000 MJ. What is its kinetic energy at that point?
6. A certain satellite has a kinetic energy of 8 billion joules at perigee (the point at which it is closest to Earth) and 5 billion joules at apogee (the point at which it is farthest from Earth). As the satellite travels from apogee to perigee, how much work does the gravitational force do on it? Does its potential energy increase or decrease during this time, and by how much?
7. Calculate the hang time of a person who moves horizontally 3 m during a 1.25-m high jump. What is the hang time when moving 6 m horizontally during this jump?
8. A horizontally moving tennis ball barely clears the net, a distance y above the surface of the court. To land within the tennis court the ball must not be moving too fast.
a. To remain within the court's border, a horizontal distance d from the bottom of the net, show that the ball's maximum speed over the net is
v= d/√ (2y/g)
b. Suppose the height of the net is 1.00 m, and the court's border is 12.0 m from the bottom of the net. Use g = 10 m/s2 and show that the maximum speed of the horizontally moving ball clearing the net is about 27 m/s (about 60 mi/h).
c. Does the mass of the ball make a difference? Defend your answer.