A child starts from rest and slides without friction from a height of h = 7.2 m

Question

A child starts from rest and slides without friction from a height of h = 7.2 m along a slide next to a pool (see figure). She is launched from a height of 1.5 m (ignore the h/5 in the figure) at an angle of 23° into the air over the pool.

What is her maximum height above the water after leaving the slide? Hint: it is possible to do this without doing projectile motion, even desirable as we are trying to learn conservation of energy; this problem does require you to use conservation of energy more than once.

Explanation / Answer

using conservation of energy

Total energy at height h = Total energy at a height h/5

K1+U1 = K2+U2

0+ m*g*h = (0.5*m*v^2)+(m*g*h/5)

m cancels on both sides

g*h = 0.5*v^2 + (g*h/5)

v is the speed before leaving the slide

0.5*v^2 = g*h(1-(1/5)) = 9.81*1.5*(1-(1/5)) = 11.772

v = 4.85 m/s

then using

hmax = v^2*sin^(theta)/(2*g) = 4.85^2*sin^2(23)/(2*9.81) = 0.183 m

then ymax = (1.5/5)+ 0.183 =0.483 m

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