Question

Tony Hawk skates down a ramp. If he is moving at 5.4 m/s at the bottom of the ramp and has a mass of 82 kg, how tall was the ramp?

Answer 1

[AI-generated answer — Explain Bot]

To determine the height of the ramp, we can use the principle of conservation of mechanical energy. At the bottom of the ramp, Tony Hawk has kinetic energy, which is given by the equation:

KE = (1/2)mv^2

Where:
- KE represents the kinetic energy
- m represents the mass (82 kg)
- v represents the velocity (5.4 m/s)

Since kinetic energy is a form of mechanical energy, it can be expressed as the sum of potential energy (PE) and kinetic energy at the top of the ramp.

In this case, at the top of the ramp, all the kinetic energy is converted into potential energy, which is given by the equation:

PE = mgh

Where:
- PE represents the potential energy
- m represents the mass (82 kg)
- g represents the acceleration due to gravity (9.8 m/s^2)
- h represents the height of the ramp (unknown)

Since the kinetic energy at the bottom of the ramp is equal to the potential energy at the top of the ramp, we can equate the two formulas:

(1/2)mv^2 = mgh

Now, we can solve for h:

h = (1/2)v^2/g

Substituting the given values:

h = (1/2)(5.4 m/s)^2 / (9.8 m/s^2)

Simplifying the equation:

h = 1.47 meters

Therefore, the height of the ramp is approximately 1.47 meters.