One more quick convervation of energy problem

[crimsonn]

Homework Statement

A skier leaves a slope with an initial speed of 5 m/s. Her speed at the bottom of the slope is 13 m/s. What is the height of the slope?

Homework Equations

PE= mgh
KE= 1/2mv^2

The Attempt at a Solution

PE + KE1 = KE2

PE=KE2-KE1

mgh = 1/2mv^2 -1/2mv^2

gh = 1/2v^2 -1/2v^2

h = 1/2mv^2 -1/2mv^2 / g

when I plug everything in, I get 14.9

the answer is 7.3


what am I doing wrong?

 

[Hootenanny]

h = 1/2mv^2 -1/2mv^2 / g

Where have these masses appeared from? If these masses are just a typo and you really used,

h = (v_i² - v_f²)/(2g)

Then you have simply plugged the numbers in wrong.

 

[baba89]

I would like to point out that there are a few things that could be improved in your solution. First, you have not included the mass (m) of the skier in your equations, which is necessary to solve for the height (h) of the slope. Secondly, you have used the wrong equation for conservation of energy. The correct equation is PE1 + KE1 = PE2 + KE2, where PE1 and KE1 represent the initial potential and kinetic energy, and PE2 and KE2 represent the final potential and kinetic energy.

Also, when solving for the height using the equation PE = mgh, you need to use the total potential energy at the top of the slope (mgh) and the final kinetic energy at the bottom of the slope (1/2mv^2). Your equation should look like this: mgh = 1/2mv^2. Finally, when solving for the height, you should divide both sides of the equation by mg, not just g. This will give you the correct answer of 7.3 meters.

In summary, to solve this conservation of energy problem correctly, you need to include the mass of the skier in your equations, use the correct conservation of energy equation, and divide both sides of the equation by mg. I hope this helps you understand the problem better and solve it correctly.