Question

A 100kg skateboarder sits at the top of a 10m half pipe ,ready to go down the ramp , what will his velocity when he is 4 m off the ground?

Answer 1

The skateboarder will have a velocity of 14 m/s when he is 4m off the ground.

Step-by-step explanation:

To find the velocity of the skateboarder when he is 4m off the ground, we can use the principle of conservation of mechanical energy. At the top of the half pipe, the skateboarder has potential energy due to his height above the ground, which will be converted into kinetic energy as he moves down the ramp.

Using the equation for potential energy (PE) and kinetic energy (KE), we have:

PE = KE

mgh = (1/2)mv^2

where m is the mass of the skateboarder (100kg), g is the acceleration due to gravity (9.8 m/s^2), h is the height of the half pipe (10m), and v is the final velocity when the skateboarder is 4m off the ground.

Substituting the given values into the equation, we can solve for v:

(100kg)(9.8 m/s^2)(10m) = (1/2)(100kg)v^2

Simplifying the equation:

9800 J = 50v^2

Dividing both sides of the equation by 50:

196 = v^2

Taking the square root of both sides:

v = 14 m/s

Therefore, the skateboarder will have a velocity of 14 m/s when he is 4m off the ground.