1. ## Help with problem

1.) A skier coasts down a very smooth, 10-m-high. If the speed of the skier on the top of the slope is 5.0 m/s, what is his speed at the bottom of the slope?

2. Use $\displaystyle U_1 + K_1 + W_{\text{other}} = U_2 + K_2$ (conservation of energy)

Or use kinematic equations (under the assumption that we have constant acceleration). It would probably be better to use energy methods.

$\displaystyle v_f = v_0 + at$

$\displaystyle x-x_0 = \frac{1}{2}(v_0 + v_f)t$

$\displaystyle x-x_0 = v_{x0}t + \frac{1}{2}at^2$

$\displaystyle v_{f}^2 = v_{0}^2 + 2a(x-x_0)$

3. Originally Posted by tukeywilliams
Use $\displaystyle U_1 + K_1 + W_{\text{other}} = U_2 + K_2$ (conservation of energy)

Or use kinematic equations

$\displaystyle v_f = v_0 + at$

$\displaystyle x-x_0 = \frac{1}{2}(v_0 + v_f)t$

$\displaystyle x-x_0 = v_{x0}t + \frac{1}{2}at^2$

$\displaystyle v_{f}^2 = v_{0}^2 + 2a(x-x_0)$
The use of the kinematic equations depends on the object having a constant acceleration. Since we aren't given any information about what the slope is like. (Yes, I know "slopes" are typically represented by lines, but I don't feel we can make that assumption in this case. We also don't have any information about the grade of the slope. As it happens the answer doesn't depend on these details, but that is a consequence of the energy theorem.)

To make a long story short, use energy methods.

-Dan