Question

If a child starts from rest at point A and lands in the water at point B, a horizontal distance L = 2.52 m from the base of the slide, determine the height h (in m) of the water slide.

Answer 1

The height of the water slide is 0.878 m

Step-by-step explanation:

Given that,

Distance = 2.52 m

Suppose Children slide down a friction less water slide that ends at a height of 1.80 m above the pool.

We need to calculate the time

Using equation of motion

`s=ut+(1)/(2)gt^2`

Put the value in the equation

`1.80=0+(1)/(2)*9.8* t^2`

`t^2=(1.80*2)/(9.8)`

`t=\sqrt{(1.80*2)/(9.8)}`

`t=0.606\ sec`

We need to calculate the velocity

Using formula of velocity

`v = (d)/(t)`

Put the value into the formula

`v=(2.52)/(0.606)`

`v=4.15\ m/s`

We need to calculate height

Using conservation of energy

`(1)/(2)mv^2=mgh`

`h=(v^2)/(2g)`

Put the value into the formula

`h=(4.15^2)/(2*9.8)`

`h=0.878\ m`

Hence, The height of the water slide is 0.878 m.