Question

1. a 79.4 kg skier loses 50% of their potential energy by the time they reach the midway point on the ski slope, which is 2.025 m high. how much energy did the skier lose?

Explanation:

Step1: Recall the formula for gravitational potential energy

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

Step2: Calculate the initial potential energy at the top of the slope

Assume the height of the full - slope is \(H\). At the mid - point, \(h=\frac{H}{2}\). The initial potential energy \(U_{i}=mgH\). But we can also calculate the energy change directly. The mass \(m = 79.4\space kg\), \(g=9.8\space m/s^{2}\), and the height change (since it's losing 50% of potential energy at the mid - point, the height considered for the energy loss is the full height of the mid - point \(h = 2.025\space m\))

$$U=mgh$$

$$U=79.4\times9.8\times2.025$$

$$U = 79.4\times19.845$$

$$U=1575.693\space J$$

Answer:

1,575,693 J