Question

Calculating Height

A ski lift is used to transport people from the base of a hill to the top. If the lift leaves the

base at a velocity of 15.5 m/s and arrives at the top with a final velocity of 0 m/s, what is the height of the hill? Round the answer to the nearest tenth.

Answer 1

To calculate the height of the hill on a ski lift, use the principle of conservation of energy and the equation for gravitational potential energy.

Step-by-step explanation:

To calculate the height of the hill, we can use the principle of conservation of energy. The initial kinetic energy of the lift at the base of the hill is converted into potential energy at the top of the hill when the final velocity is zero.

Using the equation for gravitational potential energy, we can determine the height:

PE = mgh

Where PE is the potential energy, m is the mass of the lift (assumed to be 1 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height of the hill.

Using the given information, we can calculate the height of the hill to be approximately 12.4 meters.

Answer 2

• Final velocity=v=0m/s
• Initial velocity=u=15.5m/s
• Acceleration due to gravity=g=10m/s^2
• Height=h

`\boxed{\sf v^2-u^2=2gh}`

`\\ \sf\longmapsto h=(v^2-u^2)/(2g)`

`\\ \sf\longmapsto h=(0^2-15.5^2)/(2(10))`

`\\ \sf\longmapsto h=(240.25)/(20)`

`\\ \sf\longmapsto h=12.012m`