Question

You have been asked to make a roller coaster more exciting. The owners want the speed at the bottom of the first hill doubled. How much higher must the first hill be built?

Answer 1

Answer:

The height will be 4 times.

Explanation:

Given that,

The speed at the bottom of the hill doubled.

We need to calculate the height

Using conservation of energy

$K.E_{t}+P.E_{t}=K.E_{b}+P.E_{b}$

$K.E_{b}=P.E_{t}$

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

$\dfrac{1}{2}m(4v^2)=mgh$

Therefore,

$P.E = mg(4h)$

Here, m and g are constant

Hence, The height will be 4 times.