A child starts from rest and slides without friction from a height of h the air

Question

A child starts from rest and slides without friction from a height of h the air over the pool 9.2 m along a slide next to a pool (see figure). She is launched from a height of 1.7 m (ignore the h/5 in the figure) at an angle of 270 into 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 energy conservation,

PE + KE = constant

mgh + 0 = mg(h/5) + mv^2/2

9.8 x 9.2 = (9.8 x 1.7) + v^2/2

v = 12.12 m/s

this velocity is at an angle of 27 deg above horizontal.

in vertical:

initial velcity = 12.2sin27 = 5.54 m/s

it will up until vertical velocity becomes zero.

using vf^2 - vi^2 = 2ay

0^2 - 5.54^2 = 2(-9.81)(y)

y = 1.56 m

Ymax = y + (h/5) = 1.56 + 1.7 = 3.26 m

please don't post multiple question in single post.

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