A 55-kg teenager at a water park slides down a long, winding waterslide of varyi

Question

A 55-kg teenager at a water park slides down a long, winding waterslide of varying slope. The slide has a height difference of 17m from start to finish. The teenager takes a running start, launching himself with an initial speed of 3.5m/s.

a) If the slide were frictionless, find both the teenagers kinetic energy and speed at the end of the slide.

b) If the final velocity at the end of the slide were 6.5m/s what percentage of the teenager's mechanical energy was dissipated by friction on his way down? Assume zero gravitational potential energy at the bottom of the slide.

Explanation / Answer

a) v^2 -u^2 =2gh ==> v = sqrt(3.5^2 +2*9.8*17) = > v= 18.59 m/s
and KE final = 0.5*55* (18.59)^2 = 9499.875 J

b) if final speed is 6.5m/s

then final KE = 0.5*55*6.5^2 = 1161.875 J
initial energy = 0.5*55*3.5^2 + 55*9.8*17 = 9499.875 J
change in energy = 9499.875 -1161.875 = 8388 J
% dissipated in friction = 100* 8388/9499.875 = 87.77 %

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