Question

rollercoaster track. The height of the first hill is 12.0 m and the speed of the car at the top of the first hill is 2.7 m/s.Find the height of the second hill if the speed at the top of the second hill is 5.5 m/s

Answer 1

We can use the conservation of energy:

`E1=E2`

Where:

E1 = Energy of the car in the first hill

E2 = Energy of the car in the second hill

So:

`\begin{gathered} K1+U1=K2+U2 \\ where: \\ K1=(1)/(2)mv1^2=(1)/(2)m(2.7)^2=3.645m \\ U1=mgh1=9.8(12)m=117.6m \\ K2=(1)/(2)mv2^2=(1)/(2)m(5.5)^2=15.125m \\ U2=mgh2=9.8mh2 \end{gathered}`

Therefore:

`3.645m+117.6m=15.125m+9.8mh2`

Divide both sides by m:

`\begin{gathered} 3.645+117.6=15.125+9.8h2 \\ 121.245=15.125+9.8h2 \\ 106.12=9.8h2 \\ h2=(106.12)/(9.8) \\ h2\approx10.829m \end{gathered}`

Answer:

The height of the second hill is approximately 10.829m