Question

A 54.0-kg skier starts from rest from the top of a 67-m high slope. What is the speed of the skier on reaching the bottom of the slope? (Neglect friction.)Answer: _________ m/s (round to the nearest tenth)

Answer 1

Given:

The mas of the skier is m = 54 kg

The height of the slope is h = 67 m

The skier starts from rest.

Required: The speed of the skier on reaching the bottom of the slope.

Step-by-step explanation:

As the skier was initially at rest.

The initial speed will be zero.

According to the conservation of energy, mechanical energy is constant( it is the sum of kinetic energy and potential energy)

The kinetic energy is given by the formula

`K.E.\text{ = }(1)/(2)* mass*(speed)^2`

The potential energy is given by the formula

`P.E.\text{ = mass}* acceleration\text{ due to gravity}* height`

The acceleration due to gravity is denoted by g and its value is equal to 9.8 m/s^2.

At the top of the slope, the speed is zero so the kinetic energy is zero.

Here, the entire energy is due to potential energy.

The total energy is equal to

`\begin{gathered} P.E.\text{ =54}*9.8*67 \\ =35456.7\text{ J} \end{gathered}`

At the bottom of the slope, the potential energy is zero as the height is zero.

Here, the entire energy is due to kinetic energy.

The value of kinetic energy at the bottom of the slope is equal to the potential energy at the top of the slope.

The speed at the bottom of the slope can be calculated as

`\begin{gathered} K.E.\text{ =}(1)/(2)mv^2 \\ v=\sqrt{(2K.E)/(m)} \\ =\text{ 36.2 m/s} \end{gathered}`

Final Answer: The speed of the skier at the bottom of the slope is 36.2 m/s