- #1
zeion
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Homework Statement
A sight seen on many "bunny" hills across Ontario is young skiers pushing on ski poles and gliding down a slope until they come to rest/ Observing from a distance, you note a young person (approximately 25 kg) pushing off with the ski poles to give herself an initial velocity of 3.5m/s^2. If the inclination of the hill is 5.0 degrees and the coefficient of kinetic friction for the skis on dry snow is 0.20, calculate
a) the time taken for the skier to come to a stop
b) the distance traveled down the hill
Homework Equations
V final ^2 = V initial ^ 2 + 2 a t
The Attempt at a Solution
a)
Given:
m = 25kg
V initial = 3.5 m/s^2
Angle of hill = 5 degrees
coefficient kinetic = 0.20
I need to find acceleration to use that formula to find time, acceleration down the hill with no initial velocity and just gravity is Fg parallel to the hill - Fk kinetic friction acting in the opposite direction.
Given:
m = 25kg
V initial = 3.5 m/s^2
Angle of hill = 5 degrees
coefficient kinetic = 0.20
Fg parallel to hill = mg sin 5
Fk parallel to hill = mg cos 5 0.20
Fg = (25kg)(9.8m/s^2)(sin5) = 21.35kgm / s^2 < Why are my units weird here?
Fk = (25kg)(9.8m/s^2)(cos5)(0.20) = 48.81kgm / s^2
21.35 - 48.81 = -27.46
The kinetic friction is greater than gravity parallel to hill, does that mean the skier can't move down with just gravity alone?
Or maybe the value I found for "Fk" is not kinetic friction because I think it might just be the Fn acting perpendicular to the hill. So then how do I find Fk?
Fk = Fn 0.20 ?
But I've already applied the friction coefficient to find Fn.
So then what is -27.46? Is it the acceleration parallel to hill due to gravity?
Assuming I have found the correct value for acceleration,
V final ^2 = V initial ^2 + 2at
V final is 0
V initial is 3.5m/s
t = -V initial ^ 2 / 2 a
t = (-3.5m/s)^2 / 2(-27.46m/s^2)
t = 0.22s
b)
Assuming I have found the correct value for t
d = v average t
Do I use this formula to find d?
If V final = 0 is V average = 3.5m/s + 0 / 2 = 1.75m/s?
So,
d = (1.75m/s)(0.22s)
d = 0.39m