**36**.

Tarzan grabs a vine hanging vertically from a tall tree when he is running at 9.0m/s.9.0m/s. (a) How high can he swing upward? (b) Does the length of the vine affect this height?

**37**.

Assume that the force of a bow on an arrow behaves like the spring force. In aiming the arrow, an archer pulls the bow back 50 cm and holds it in position with a force of 150N. If the mass of the arrow is 50g and the “spring” is massless, what is the speed of the arrow immediately after it leaves the bow?

**31**.

A boy throws a ball of mass 0.25kg0.25kg straight upward with an initial speed of 20m/s20m/s When the ball returns to the boy, its speed is 17m/s17m/s How much much work does air resistance do on the ball during its flight?

**32**.

A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance?

**34**.

A 1.0-kg ball at the end of a 2.0-m string swings in a vertical plane. At its lowest point the ball is moving with a speed of 10 m/s. (a) What is its speed at the top of its path? (b) What is the tension in the string when the ball is at the bottom and at the top of its path?

**35**.

Ignoring details associated with friction, extra forces exerted by arm and leg muscles, and other factors, we can consider a pole vault as the conversion of an athlete’s running kinetic energy to gravitational potential energy. If an athlete is to lift his body 4.8 m during a vault, what speed must he have when he plants his pole?

**39**.

A sled of mass 70 kg starts from rest and slides down a 10°10° incline 80m80m long. It then travels for 20 m horizontally before starting back up an 8°8° incline. It travels 80 m along this incline before coming to rest. What is the magnitude of the net work done on the sled by friction?

**40**.

A girl on a skateboard (total mass of 40 kg) is moving at a speed of 10 m/s at the bottom of a long ramp. The ramp is inclined at 20°20° with respect to the horizontal. If she travels 14.2 m upward along the ramp before stopping, what is the net frictional force on her?

**41**.

A baseball of mass 0.25 kg is hit at home plate with a speed of 40 m/s. When it lands in a seat in the left-field bleachers a horizontal distance 120 m from home plate, it is moving at 30 m/s. If the ball lands 20 m above the spot where it was hit, how much work is done on it by air resistance?

**46**.

A single force F(x)=−4.0xF(x)=−4.0x (in newtons) acts on a 1.0-kg body. When x=3.5m,x=3.5m, the speed of the body is 4.0 m/s. What is its speed at x=2.0m?