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?
------------------------------------
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
-------------------------------------
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?
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
This answer still shows up as incorrect
Your answer is incorrect because you used the wrong value for H. The equation gH = change in (V^2)/2 relates the change in potential energy (mgh) to the change in kinetic energy (1/2 mv^2) as the skier moves from the top to the bottom of the incline.
To find H, we need to rearrange this equation and solve for it. Here's the correct approach:
1. Convert the slope angle from degrees to radians: θ = 13.1° * (π/180°) ≈ 0.229 radians.
2. Use the conservation of energy equation and substitute the given values:
mgh = (1/2) mv^2, where m is the mass of the skier.
3. Simplify the equation by canceling out the mass m:
gh = (1/2) v^2
4. Solve for H:
H = (1/2) v^2 / g
5. Plug in the given values:
H = (1/2) * (18.8 m/s)^2 / (9.8 m/s^2) ≈ 18.14 m
Now that we have H, we can find the length L of the incline using the formula H/L = sin θ:
L = H / sin θ
= 18.14 m / sin 0.229
≈ 79.06 m
Therefore, the correct length of the incline is approximately 79.06 meters.