A runaway ski slides down a 290-m-long slope inclined at 38.0 degree with the ho

Question

A runaway ski slides down a 290-m-long slope inclined at 38.0 degree with the horizontal. If the initial speed is 13.0 m/s, how long does it take the ski to reach the bottom of the incline if the coefficient of kinetic friction between the ski and snow is 0.100? (Express your answer to two significant figures.) S Submit If the initial speed is 13.0 m/s, how long does it take the ski to reach the bottom of the incline if the coefficient of kinetic friction between the ski and snow is 0.150? (Express your answer to two significant figures.) S Submit

Explanation / Answer

1) friction force = uN = u mgcos@

Fnet = mgsin@ - umgcos@ = m [ (9.81 x sin38) - (0.1 x 9.81 x cos38) ]

= 5.27m

a = Fnet / m = 5.27 m/s^2

using v^2 - u^2 = 2ad

v^2 - 13^2 = 2(5.27)(290)

v = 56.78 m/s

v = u + at

56.78 = 13 + 5.27t

t = 8.31 s

2) now Fnet = mgsin@ - umgcos@ = m [ (9.81 x sin38) - (0.15 x 9.81 x cos38) ]

= 4.88m

a = Fnet / m = 4.88 m/s^2

using r = ut + at^2 /2

290 = 13t + (4.88 t^2 /2 )

2.44t^2 + 13t - 290 = 0

t = 8.56 s

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