Hi! I have some questions from a study guide in my physics class, and they give me the answer, but I have to show how to get the answer. I did most of them, but need help with these. Here is problem #1:

A skier with a mass of 60.0 kg is standing at the top of a snow covered hill. As he slides down the hill, his height decreases by 42 m over a distance of 100 m of travel. How fast will he be going at the bottom of the hill (assuming no friction)? (28.7 m/s)

mgh=mv²/2

v=sqrt(2gh)=...

To solve this problem, we can use the principle of conservation of energy. The initial potential energy at the top of the hill is converted into kinetic energy at the bottom of the hill.

The potential energy at the top of the hill can be calculated using the equation: P.E. = m * g * h, where m is the mass of the skier (60.0 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height (42 m).

P.E. = 60.0 kg * 9.8 m/s² * 42 m = 24696 J

This potential energy is converted entirely into kinetic energy at the bottom of the hill. The formula for kinetic energy is: K.E. = 0.5 * m * v², where m is the mass of the skier and v is the speed at the bottom of the hill.

We can equate the potential energy to the kinetic energy:
24696 J = 0.5 * 60.0 kg * v²

Simplifying the equation, we get:
24696 J = 30.0 kg * v²
v² = 24696 J / 30.0 kg
v² = 823.2 m²/s²

Taking the square root of both sides, we find:
v = √(823.2 m²/s²)

v ≈ 28.7 m/s

Therefore, the skier will be going at a speed of approximately 28.7 m/s at the bottom of the hill.