A skier of mass 102.4 kg is skiing down a frictionless mountain trail. The skier

Question

A skier of mass 102.4 kg is skiing down a frictionless mountain trail. The skier begins with an initial velocity of 8.1 m at point A, which has a total height s of 112 m and makes an angle of 32? with the horizontal axis. At point B, which has a height of 54 m, the train is flat with the horizontal. The trail is flat for 14 m and then slopes downward at an angle of 18? to point C, which is at the bottom of the hill (height = 0).

• a)Find the velocity of the skier at point B

• b)Find the velocity of the skier at the bottom of the hill

• c)How would your answers differ if friction taken in to account?

Explanation / Answer

(A) Applying energy conservation,

PE_a + KE_a = PE_b + KE_b

m g hA + m Va^2 /2 = m g hB + m vB^2 /2

(9.8 x 112) + (8.1^2 / 2) = (9.8 x 54) + vB^2 /2

vB = 34.7 m/s .....Ans

(B) again for A and C.

(9.8 x 112) + (8.1^2 / 2) = 0 + vC^2 /2

vC = 47.5 m/s

(C) if friction is there then some of energy wil be lost against friction.

then values of vB and vC will be less what we got.

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