physics question

Question

A skier weighing 82.8kg starts from rest and slides down a 32.0m frictionless slope that is inclined at an angle of 15 degrees with the horizontal. Ignore air resistance. Calculate the work done by gravity on the skier in kJ.

Answer 1

The work done in moving an object from one height to another against the force of gravity is...

W = PE = mgh = 82.8 kg * 9.81 m/s^2 * h

We know m and g, but need to calculate h...

The height can be calculated by...

sin theta = opposite / hypotenuse = h / slope_length, so...

h = slope_length * sin 15º

h = 32.0 * sin 15º ≈ 32.0 * 0.258819 ≈ 8.2822

h ≈ 8.28 m (3 sig figs)

So now we have (question has a sense of humor: mass and height have 828 in them)

W = 82.8 kg * 9.81 m/s^2 * 8.28 m ≈ 6726 N-m ≈ 6730 N-m (3 sig figs)

W = 6.73 kJ (3 sig figs) (ANSWER)