In a downhill ski race surprisingly little advantage is gained by getting a runn

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 35° 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.)

Part One (a) starting from rest final speed (m/s)

(b) time taken (s )

Part 2 (a) starting with an initial speed of 2.50 m/s final speed (m/s)

(b) time taken (s)

Explanation / Answer

We equations of motion along the incline; along the incline accleration = g*sin(q) ;q is the angle of slope

Part One] a) using equation of motion : V2 - u2 = 2*a*S

V2 - 0 = 2*g*sin(35o)*75 =====> V = 29.05198 m/s2

b) using equation of motion: V = u + a*t

29.05/(9.81*sin(35)) = t = 5.163158712 sec

part 2) a) using equation of motion : V2 - u2 = 2*a*S

V2-2.52 = 2*9.81*sin(35)*75 ===> V= 29.15935058 m/s

b) using equation of motion: V = u + a*t

29.159 = 2.5 + 9.81*sin(35)*t

t = 4.737936732 sec.

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