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

Answer:

The height of the water slide is 0.878 m

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

$s=ut+\dfrac{1}{2}gt^2$

Put the value in the equation

$1.80=0+\dfrac{1}{2}\times9.8\times t^2$

$t^2=\dfrac{1.80\times2}{9.8}$

$t=\sqrt{\dfrac{1.80\times2}{9.8}}$

$t=0.606\ sec$

We need to calculate the velocity

Using formula of velocity

$v = \dfrac{d}{t}$

Put the value into the formula

$v=\dfrac{2.52}{0.606}$

$v=4.15\ m/s$

We need to calculate height

Using conservation of energy

$\dfrac{1}{2}mv^2=mgh$

$h=\dfrac{v^2}{2g}$

Put the value into the formula

$h=\dfrac{4.15^2}{2\times9.8}$

$h=0.878\ m$

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