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 25

Answer 1

a)We are neglecting the friction, so remaining force exerted by the track is the normal force, which is perpendicular to the direction of motion. And this normal force does no work. The net work on the skier is then done by gravity alone. The loss of gravitational potential energy from moving downward through a distance h equals the gain in kinetic energy. Using equations for PE and KE, we can solve for the final speed v, which is the desired quantity.

From Rest position:

Potential Enegy = Kinetic Energy
mgh = 1/2m V²

V=final velocity.

h=height

height can be find out by,h=75sin25⁰=31.69
m is common in both sides. Cancel out the m
9.8 x 31.69 = 310.62

310.62= 0.5 V²

and V = 24.92 m/s

b)With Initial velocity of 2.0 m/s:
Change in Kinetic energy = Change in Potential Energy
1/2 m V₂² - 1/2 V₁² = mgh
1/2 m V₂² - 1/2 m (2.0)² = m ( 310.62)

m is also common here, so Cancel out the m
0.5 V₂² = 310.62 -2 = 308.62
V₂ = 24.84 m/s