A 73 kg skier coasts up a hill at 9.3 degrees to the horizontal. Determine how far along the...hill the skier slides before stopping, if the...

The kinetic energy that the skier has at the bottom of the hill
is converted to gravitational potential energy as he moves up. The skier would stop when the
kinetic energy has reduced to zero and it has been entirely converted to potential
energy.

Kinetic energy is given by (1/2)*m*v^2. Using the
information provided, it is (1/2)*73*(4.2)^2.

The potential energy
is given by m*g*h, where m is the mass, g is the acceleration due to gravity and h is the
height.

So we have (1/2)*73*(4.2)^2 =
73*9.8*h

=> (1/2)*(4.2)^2 =
9.8*h

=> h =
(1/2)*(4.2)^2/9.8

As the slope is 9.3 degrees, the distance D moved
up the slope is related to the height by h/D = sin 9.3

=> D =
h/sin 9.3

=> D = [(1/2)*(4.2)^2/9.8]/sin
9.3

=> D = (1/2)*(4.2)^2/(9.8*sin
9.3)

solving for D we get,

=> D
= 5.56 m

The skier can slide 5.56 m up the slope
before he comes to a halt.