n a downhill ski race surprisingly little advantage is gained by getting a runni

Question

n 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 60.0 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.) (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

Explanation / Answer

A) initial velocity is u = 0 m/s

final velocity is v = ?

accelaration a = g*sin(35) = 9.8*sin(35) = 5.62 m/s

apply law of conservation of energy

m*g*h = 0.5*m*v^2

v = sqrt(2*g*h) = sqrt(2*9.81*60*sin(35)) = 25.98 m/s

time taken is t = v/(g*sin(35)) = 25.98/(9.81*sin(35)) = 4.61 S

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B) apply law of conservation of enertgy

m*g*h + 0.5*m*u^2 = 0.5*m*v^2

9.81*60*sin(35) + 0.5*2*2 = 0.5*v^2

v = 26.06 m/s

apply v = u+(a*t)

t = (v-u)/(g*sin(35)) = (26.06-2)/(9.81*sin(35)) =4.27 S

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