Similar to the problem worked in class, Sam (80 kg) takes off up a 60 m high, 10

Question

Similar to the problem worked in class, Sam (80 kg) takes off up a 60 m high, 10° slope on his jet-powered skis. The coefficients of kinetic and static friction between the skis and the ramp are 0.30 and 0.50, respectively. The skis have a thrust of 250 N and remain tilted at 10° throughout the problem. When Sam is in the air, he experiences a drag force due to the wind of 70 N.

a. What is the net force acting on Sam as he travels up the ramp?

b. What is Sam’s acceleration which he is on the ramp?

c. How far does Sam land from the base of the cliff?

Explanation / Answer

Hieght, h = 60m
Slope angle, theta =10
mass, m = 80kg
Thrust, T = 250N

T - mgsin(theta) - f = ma
f = mu N
N = mgcos(theta)
T - mgsin(theta) - mu*mgcos(theta) = ma

check for static friction:

250 - 80*9.8*sin(10) - 0.5*80*9.8*cos(10) = 80*a
250 - 136.14 - 386.044 = 80*a -> Negative acceleration, hence the ski should not move as it would not be able to overcome the static friction

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