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 \(U = mgh\), where \(U\) is potential energy, \(m\) is mass, \(g\) is acceleration due to gravity (\(g = 9.8\space m/s^{2}\)), and \(h\) is height.

Step2: Rearrange the formula to solve for mass

We need to solve \(U = mgh\) for \(m\). So, \(m=\frac{U}{gh}\).

Step3: Substitute the given values

Given \(U = 137200\space J\), \(h = 200\space m\), and \(g = 9.8\space m/s^{2}\).

$$ m=\frac{137200}{9.8\times200} $$

First, calculate \(9.8\times200=1960\).
Then, \(m=\frac{137200}{1960}=70\space kg\)

Answer:

70 kg