Question

A diver with a mass of 70.0 kg stands motionless at the top of a 3.0 m high diving platform. Calculate the potential energy relative to the water surface while standing on the platform, and his speed when he enters the pool?

Answer 1

The potential energy of the diver while standing on the platform is 2058 J. The speed of the diver when he enters the pool is 8.19 m/s.

Step-by-step explanation:

To calculate the potential energy of the diver while standing on the platform, we can use the formula:

Potential Energy = mass * acceleration due to gravity * height

Given that the mass of the diver is 70.0 kg, the acceleration due to gravity is 9.8 m/s^2, and the height of the platform is 3.0 m, we can calculate the potential energy as:

Potential Energy = 70.0 kg * 9.8 m/s^2 * 3.0 m = 2058 J

To calculate the speed of the diver when he enters the pool, we can use the principle of conservation of energy. The potential energy at the top of the platform is converted into kinetic energy as the diver falls. Using the formula:

Kinetic Energy = 0.5 * mass * velocity^2

Since the potential energy and kinetic energy are equal, we can equate the formulas:

2058 J = 0.5 * 70.0 kg * velocity^2

Solving for velocity, we find:

velocity = sqrt(2 * (2058 J / 70.0 kg)) = 8.19 m/s