Question

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0m long. His speed at the bottom of the swing is 8m/s. What is the maximum height Tarzan reaches during the swing?

1) 5.0 m
2) 6.0 m
3) 7.0 m
4) 8.0 m

Answer 1

Tarzan reaches a maximum height of 16.7 m during the swing.

Step-by-step explanation:

To find the maximum height Tarzan reaches during the swing, we can use the conservation of mechanical energy. At the bottom of the swing, Tarzan's speed is 8 m/s. We know that the total mechanical energy is conserved, so the initial mechanical energy at the bottom of the swing is equal to the mechanical energy at the maximum height.

At the bottom of the swing, the mechanical energy is given by the sum of kinetic energy (1/2 * mass * velocity^2) and potential energy (mass * gravity * height). Since Tarzan starts from rest at the bottom of the swing, the kinetic energy is zero. Therefore, at the maximum height, the mechanical energy is equal to the potential energy:

0.5 * mass * velocity^2 + mass * gravity * height = mass * gravity * (2 * length of the vine)

Since we are given the length of the vine (10.0 m) and the speed at the bottom of the swing (8 m/s), we can solve the equation for the height:

0.5 * mass * 8^2 + mass * 9.8 * height = mass * 9.8 * 20.0

0.5 * 64 + 9.8 * height = 9.8 * 20

32 + 9.8 * height = 196

9.8 * height = 196 - 32

9.8 * height = 164

height = 164 / 9.8 = 16.7 m

Tarzan reaches a maximum height of 16.7 m during the swing.