Question

A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. As the drawing shows, one person hits the water 5.00 m from the end of the slide in a time of 0.270 s after leaving the slide. Ignore friction and air resistance, find the height H in the drawing.

Answer 1

17.86 m

Step-by-step explanation:

The first step is to find the velocity of the swimmer.

Velocity, v = s/t

Velocity, v = 5 / 0.27

Velocity, v = 18.52 m/s

Then, we find the height

h = ½gt²

h = ½ * 9.8 * 0.27²

h = 4.9 * 0.0729

h = 0.36 m

Next, we apply the law of conservation of energy

mgH = mgh + ½ mv²

9.8Hm = m(9.8 * 0.36 + 0.5 * 18.52²)

9.8H = 3.528 + 171.4952

9.8H = 175.02

H = 175.02 / 9.8

H = 17.86 m

Therefore, the needed height is 17.86 m