Tarzan, an 85 Kg jungle brute, was running along a branch at a speed of 7.5 m/s 15 m above a level jungle floor. He grabs a 17 m vine and swings up to the maximum height where he grabbed a 25 m vine hanging at a 45o angle and swung on. At the bottom of the swing he let go and landed on the edge of the level jungle floor right on a large banana leaf at the top of a 38o hill and he slid down the hill without friction for a total distance of 85 m where the hill ended in a 25m cliff with a lagoon below. If he landed in the water and dove straight in to a depth of 3.2 m, what was his speed when he hit the water?

Question

Tarzan, an 85 Kg jungle brute, was running along a branch at a speed of 7.5 m/s 15 m above a level jungle floor. He grabs a 17 m vine and swings up to the maximum height where he grabbed a 25 m vine hanging at a 45o angle and swung on. At the bottom of the swing he let go and landed on the edge of the level jungle floor right on a large banana leaf at the top of a 38o hill and he slid down the hill without friction for a total distance of 85 m where the hill ended in a 25m cliff with a lagoon below. If he landed in the water and dove straight in to a depth of 3.2 m, what was his speed when he hit the water?

Answer 1

To find Tarzan's speed when he hit the water, let's break down the problem into different parts and calculate each step.

1. Swinging on the vine:
Tarzan swings from a 17 m vine to a 25 m vine at a 45o angle. To calculate his speed at the top of the swing, we need to use the conservation of mechanical energy.

The potential energy at the top of the swing can be calculated as:
Potential Energy = Mass * Gravity * Height

Tarzan's potential energy at the top of the swing:
Potential Energy = 85 kg * 9.8 m/s^2 * (15 m + 25 m) = 85 kg * 9.8 m/s^2 * 40 m

At the top of the swing, all potential energy is converted to kinetic energy since Tarzan is at the highest point. So, we have:
Potential Energy = Kinetic Energy
85 kg * 9.8 m/s^2 * 40 m = (1/2) * Mass * Velocity^2

Rearranging the equation and solving for velocity:
Velocity^2 = (85 kg * 9.8 m/s^2 * 40 m) / (1/2 * 85 kg)
Velocity = √( (85 kg * 9.8 m/s^2 * 40 m) / (42.5 kg) )

Calculate the velocity using this formula.

2. Sliding down the hill:
Tarzan slides down a hill without friction, so no energy is lost to friction.
The potential energy at the top of the hill (at the banana leaf) is converted to kinetic energy at the bottom of the hill.

The initial potential energy at the top of the hill can be calculated as:
Potential Energy = Mass * Gravity * Height

Tarzan's potential energy at the top of the hill:
Potential Energy = 85 kg * 9.8 m/s^2 * 85 m = 85 kg * 9.8 m/s^2 * 85 m

At the bottom of the hill, all potential energy is converted to kinetic energy. So:
Potential Energy = Kinetic Energy
85 kg * 9.8 m/s^2 * 85 m = (1/2) * Mass * Velocity^2

Rearranging the equation and solving for velocity:
Velocity^2 = (85 kg * 9.8 m/s^2 * 85 m) / (1/2 * 85 kg)
Velocity = √( (85 kg * 9.8 m/s^2 * 85 m) / (42.5 kg) )

Calculate the velocity using this formula.

3. Hitting the water:
Tarzan then jumps off the cliff and lands in the water. The vertical distance he dives can be calculated using the depth.

Tarzan's vertical diving distance = Depth = 3.2 m

To calculate his speed when hitting the water, we need to use the equation of motion:
Velocity^2 = Initial Velocity^2 + 2 * Acceleration * Displacement

Since Tarzan jumps vertically, his initial velocity is zero; we have:
Velocity^2 = 0 + 2 * Acceleration * Depth

Solving for velocity:
Velocity = √( 2 * Acceleration * Depth )

Calculate the velocity using this formula.

Now that you have the velocities calculated at each step, you can determine Tarzan's speed when he hit the water by taking the final velocity from the diving step.