How does the starting height of a ski ramp affect the distance travelled after taking off?
I need detailed theory on it, but I don't know and can't find it anywhere:')
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- Thread Starter
- 12-02-2016 12:22
- 12-02-2016 12:37
If it tarts at height h, it has gravitational potential energy of GPE=mgh. If the height of the ramp is r, then it loses GPE of mg(h-r), where h-r is the change in height. This is converted into kinetic energy, which is given by KE=1/2mv^2. 1/2mv^2=mg(h-r) can be rearranged to give v=sqrt(2g(h-r)).
This velocity will be at the angle of the end of the slope, which i will call a. This gives it a horizontal component of velocity of vcosa and a vertical component of vsina. You know it will accelerate to the ground at g ms^-2. Considering the vertical motion, you can use s=ut+1/2at^2 to find the time t to fall to the ground, and then use the same equation for the horiztonal motion you can calculate the distance it travels.
Hope that helps, and i typed this on a phone so be careful of me making typos.