A skier is gliding along at 1.13 m/s on horizontal, frictionless snow. He suddenly starts down a 13.1° incline. His speed at the bottom is 18.8 m/s. What is the length of the incline?
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Use his change in kinetic energy to get his loss of potential energy. The equation
g H = change in (V^2)/2
can be used to het the height change, H.
H and the slope angle can be used to get the length L of the incline.
H/L = sin 13.1
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My attempt:
H/L = sin 13.1
L = sin13.1 / H
= sin13.1 / 18.8 m/s
= 0.01 km = 10 m
Why is this answer incorrect?
Responses
physics - drwls, Wednesday, October 8, 2008 at 2:10am
Your equation L = sin13.1 / 18.8 m/s
is totally wrong. You cannot have a length on one side of an equation and 1/Velocity on the other side. It is not even dimensionally correct. You did not follow the method suggested. Where did the L = 0.01 km come from?
The change in V^2/2 is (18.8^2 - 1.13^2)/2 = 176.1 m^2/s^2
That equals the change in gH
The change in H is therefore
176.1 m^2/s^2 / 9.8 m/s^2 = 18.0 m
physics - Luckna, Wednesday, October 8, 2008 at 9:35am
This answer still shows up as incorrect
I computed H for you. They asked for the length L of the incline. Did you do the final step to get L?
We usually don't do complete answers for students. We try to teach you the method to solve problems yourself.
I agree with DrWLS.
Can i have the formula for this step please?
You know h is the height, you know the angle, and you are looking for the hypotenuse. Could the formula be the sine function?
h =18.0 m
angle = 13.1°
hypotenuse = ?
Sine function formula is:
Opposite / hypotneuse
What is opposite?
The correct equation to use in this problem is:
gH = (V_f^2 - V_i^2)/2
Where:
g is the acceleration due to gravity (9.8 m/s^2),
H is the change in height,
V_f is the final velocity (18.8 m/s), and
V_i is the initial velocity (1.13 m/s).
Therefore, the change in height can be calculated as:
H = (V_f^2 - V_i^2)/(2g)
H = (18.8^2 - 1.13^2)/(2*9.8)
H = (352.64 - 1.2769)/19.6
H = 351.3631/19.6
H = 17.9 meters
Next, you can use the slope angle, which is 13.1 degrees, and the change in height to find the length of the incline. The formula for this is:
H/L = sinθ
Where:
L is the length of the incline, and
θ is the slope angle (13.1 degrees).
Rearranging the formula, you get:
L = H/sinθ
L = 17.9/sin13.1
L = 101.57 meters
The correct answer for the length of the incline is approximately 101.57 meters.