Question

The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 5.4 m/s. Neglect nonconservative forces, such as friction and air resistance, and find the height h of the highest point reached by the skateboarder on the right side of the ramp

Answer 1

Concepts and reason

The concepts used to solve this problem are potential energy, conservation of energy and kinetic energy.

Initially, use the potential energy and kinetic energy of the skateboard that reaches at the highest point on the right side of the ramp. Then, use the principle of conservation of energy to compare the kinetic and potential energy to find the height of the skateboard that reaches at the highest point.

Fundamentals

There is no friction acts on the skateboard. When the skateboard reaches the top on the right side of the ramp, it gains kinetic energy.

The expression for the kinetic energy of the skateboard is,

Here, m is the mass of the skateboard and v is the initial speed of the skateboard that starts from the left side of the ramp.

Since, the skateboard reaches at the maximum height on the right side of the ramp, setting the top of the ramp as zero, the potential energy remains conserved.

The expression for the potential energy of the skateboard is,

Here, m is the mass of the skateboard, h is the height of the skateboard that reaches on the right side of the ramp and g is the acceleration due to gravity.

According to the principle of conservation of energy,

According to the principle of conservation of energy,

Substitute for and for to find height.

The expression for the maximum height reached by the skateboarder,

Substitute for and for to find h.

Ans:

The height of the highest point reached by the skateboarder is .