A skier is traveling at a speed of 34.7 m/s when she reaches the base of a frictionless ski hill. This hill makes an angle of 10^o with the horizontal. She then coasts up the hill as far as possible. What height (measured vertically above the base of the hill) does she reach?

h = 61.5m

Explanation:

Initial speed = 34.7m/s

Net force =

F= -mg Sin 10

We are finding distance moved by this skier upon the hill.

ma = - mgSin10

a = -gSin10

g = 9.8

Sin 10 = 0.1564

a = -9.8(0.1564)

a = -1.53

This is the acceleration

(-34.7)² = 2as

= -34.7² = (-2x1.53)s

-1204.09 = -3.06s

We find the value of s

S = -1204.09/-3.06

S = 393.5m

Sin10 = h/393.5m

0.1564 = h/393.5m

h = 0.1564x393.5m

h = 61.5

when the velocity of a mass on a spring is zero, the acceleration is at a maximum .