posted by alex .
Fred and George who are identical twins (same body mass) are competing in aerial skiing. Fred hits the take off with a speed of 20 whereas George has a speed of 8.5. How much higher will Fred go?
consider the takeoff to be at (0,0). The height of the skier is thus
y = vt - 4.9t^2
maximum height is thus reached at t = v/9.8
y(v/9.8) = v*v/9.8 - 4.9(v/9.8)^2
= v^2/9.8 - v^2/(4*4.9)
= v^2/9.8 (1 - 1/2)
Since the max height is directly proportional to the square of the takeoff velocity, the ratio of the max heights achieved by Fred and George is (20/8.5)^2
Since you give no data regarding the angle of takeoff, we cannot calculate any absolute values, but we do have the ratio.