Question

You are on a sled at the top of a hemispherical, snowy hill of radius 13 m. You begin to slide down the hill. How fast are you moving in m/s when you have made it 14 degrees down the hemisphere as seen below?

Answer 1

Answer:

Explanation:

There will be loss of potential energy due to loss of height and gain of kinetic energy .

loss of height = R - R cos 14 ,    R is radius of hemisphere .

R ( 1 - cos 12 )

= 13 ( 1 - .978 )

h = .286 m

loss of potential energy

= mgh

= m x 9.8 x .286

= 2.8 m

gain of kinetic energy

1/2 m v ² = mgh

v² = 2 g h

v²  = 2 x 9.8 x 2.8

v = 7.40 m /s

Answer 2

Answer:

13.90 m/s

Explanation:

from the diagram in the attachment

we can find height h

 $h=rsin14=13sin14\\=3.15 m$

now by energy conservation at two points we can write

velocity at 14 degrees down the hemisphere

$v=\sqrt{2g(13-3.14)} =\sqrt{2\times9.81\times9.86} \\=13.90\text{ m/s}$