7:19 PM Ski Jump. A skier starts from rest at height H above the end of a ski-ju

Question

7:19 PM Ski Jump. A skier starts from rest at height H above the end of a ski-jump ramp (see figure below) and leaves the ramp at an angle . Neglect the effects of air resistance and assume the ramp is frictionless. Applying the equations of projectile motion to the skier once she leaves the ramp, find algebraically an expression for the maximum height of this jump above the end of the ramp, h in terms of H and . a. b. Now assume that friction and air resistance are important. (i) Label on the figure below the point or points on the skier's path where these two non-conservative forces have their maximum magnitude. () Will the maximum height h'of the jump still be the same as the h you found in par a? Explain why or why not using your own words and/or equations. End of ramp

Explanation / Answer

given initial height = H

angle of projectile = theta

a. speed of the ski diver at the starting of the ramp = v

now from conservation of energy, for skidiver of mass m

0.5mv^2 = mgH

v = sqroot(2gH)

now. maximum height = h

then

2*g*h = (vsin(theta))^2 = 2gH*sin^2(theta)

h = H*sin^2(theta)

b. if friction and air resistance are important

the air resistance will be maximum at the lowest point beofre the dive as the speed of the diver is highest at this point

the friction force will remain fairly constant throughout the ride as friction force depends on normal reaction force which will remain constant if the angle of the slope of the incline is constsnt

this friction will do work against the motion, consuming some energy and hence the end speed of the ski diver v' will be less than v, and hence the final height h' is going to be lesser than h

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