Coasting from rest down a certain hill...?

Question

Coasting from rest down a certain hill, whose slope is variable, I reach a speed of 13.89 m/s at the bottom. If I coast from rest down the first half of the hill I reach a speed of 12 m/s. Ignoring the effects of air resistance and friction:
•How fast would I therefore be going if I coasted from rest down the second half of the hill?
•How high would I have to climb from the bottom of the hill to reach the halfway point?

Answer 1

I think I've understood the question, hope it's correct :

The height or the highest altitude of the hill will be : H

At the midpoing, the altitude will be : h

So then, let's use the conservation of energy for the first question :

You reached 13.89 m/s when you started at "H", so :

m*g*H = m*v^2 / 2

v = 13.89

9.8 = gravity

H = 9.8 (meters)

If you started from rest down the first half of the hill, then you are in "h" :

m*g*H = mgh + m*144 / 2

here, we have to use the maximum altitude : H and the altitude at the midpoint that we set it was : h

gH = gh + 72

h = 2.45 meters

And, if you wanna find how fast would you be going, if you start from the rest during the second half of the hill :

mgh = mv^2 / 2

yes, that's it, know we use "h"

9.8*2.45 = v^2 / 2

v = 6.92 m/s

hope that help you