Question

Determine the stopping distance for a skier moving down a slope with friction with an initial speed of 20.0 m/s (See the following Figure). Assume (kinetic friction coefficient) µK _=0.180 and ?=5.00°.

Answer 1

Final velocity^2 = Initial velocity^2 + 2 * a * d
0 = 20.0^2 + 2 * a * d

Determine acceleration from the net force.
Force parallel = mass * g * sin ?
Friction force = µ * mass * g * cos ?
Net force = mass * g * sin ? – µ * mass * g * cos ?

Acceleration = net force ÷ mass

Acceleration = g * sin ? – µ * g * cos ? = g * (sin ? – µ * cos ?)
Acceleration = 9.8 * (sin 5.00 – 0.180 * cos 5.00) = -0.9031 m/s^2

0 = 20.0^2 + (2 * -0.9031 * d)
2 * 0.9031 * d = 20.0^2
d = 20.0^2 ÷ (2 * 0.9031)

d = 221.45m