Question

you have been hired 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

What's the formula for kinetic energy? It is
\[ KE = \frac{1}{2}mv^2 \]
If we double the speed at the bottom from v to 2v, the KE changes to KE'
\[ KE \ ' = \frac{1}{2}m(2v)^2 = 2mv^2 = 4KE \]

In other words, the kinetic energy increases by a factor 4.

Now, that being the case, how much higher does the hill have to be?

Answer 2

As when there is no change in velocity it's kinetic energy is 1/2mv^2.where v is velocity and m is mass when velocity is doubled then kinetic energy will be 4 times using above formula.i.e kinetic energy increases four times to previous value...and calculate what you want...

Answer 3

is the answer four times?