Question

a skier with a potential energy of 137,200 j waits on top of a ski jump that is 200 m high. what is the mass of the skier?
20 kg
70 kg
137 kg
686 kg

Explanation:

Step1: Recall the formula for gravitational potential energy

The formula for gravitational potential energy is \( PE = mgh \), where \( PE \) is potential energy, \( m \) is mass, \( g \) is the acceleration due to gravity (we use \( g = 9.8 \, \text{m/s}^2 \) for this problem), and \( h \) is height. We need to solve for \( m \), so we rearrange the formula to \( m=\frac{PE}{gh} \).

Step2: Substitute the given values into the formula

We know that \( PE = 137200 \, \text{J} \), \( g = 9.8 \, \text{m/s}^2 \), and \( h = 200 \, \text{m} \). Substituting these values into the formula for \( m \), we get:
\( m=\frac{137200}{9.8\times200} \)

Step3: Calculate the denominator first

Calculate \( 9.8\times200 = 1960 \).

Step4: Divide the potential energy by the result from Step3

Now, divide \( 137200 \) by \( 1960 \): \( \frac{137200}{1960}=70 \).

Answer:

70 kg (corresponding to the option "70 kg")