Question

In a downhill ski race surprisingly little advantage is gained by getting a running start. This is because the initial kinetic energy is small compared with the gain in gravitational potential energy even on small hills. To demonstrate this, find the final speed and the time taken for a skier who skies 75.0 m along a 30° slope neglecting friction for the following two cases. (Note that this time difference can be very significant in competitive events so it is still worthwhile to get a running start.)

(a) starting from rest final speed ._______ m/s

time taken__________ s

(b) starting with an initial speed of 2.00 m/s

final speed__________ m/s

time taken__________ s

Answer 1

Skier started at A travel distance to point B. Using trigonometry, the height of point A is

Let v_i and v_f be the initial and the final speeds. The initial height is h_i=h=l/2 and the final height is h_f=0. If we neglect friction, the mechanical energy of the skier is conserved.

Using h_f=0 and h_i=l/2

To find the time of the journey we use kinematics equations. Let a be the acceleration of the skier

Using (1)

Using kinematics equation

(a)

Initial speed v_i=0. To find final speed we use (2)

To find time we use (3)

(b)

Initial speed v_i=2.00m/s. To find final speed we use (2)

To find time we use (3)