potential energy and energy conservation

Question

I already found #1MEo, just need #2 height please.

A 50.9 kg child slides down a water slide with a velocity of 1 m/sec at the top. At the bottom of the slide, she is moving horizontally, y=2 meters above the water. She splashes into the water d=2.5 meters to the left of the bottom of the slide.

1) Assuming potential energy to be zero at the water level, what is the mechanical energy of the child at the top of the slide?

ME_o= 1386.72J  

2)

How high is the top of the slide above the bottom of the slide?

h =

Answer 1

Hello Alanis,

You can solve this in one of the two ways.

Method 1:

Since you calculated total energy at top of slide as 1387 joules. This equals kinetic energy + potential energy at top point. Kinetic energy at top is 25.45 joules calculated as 1/2 * 50.9 * 1²

Potential energy at the top point is therefore 1387 - 25.45 = 1361.55 joules. You can derive height at top point by the potential energy equation mgh = 1361.55 which gives h = 2.73 m. This is the height from water level. Since the bottom of slide is 2 m from water level, the top of slide is 0.73 m from bottom

Method 2:

While arriving at total energy at top of the slide you would have derived kinetic energy at bottom of the slide as 399 joules. This kinetic energy = initial kinetic energy + potential energy difference between top of the slide and bottom.

25.45 + potential energy = 399

mgh = 373.6 where h is the height from top of slide to bottom

h = 0.74 m

Hope this helps. Do not hesitate to reach out for any followup questions