Question

A rollercoaster cart with a mass of 337 kg travels along a 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/sSolve using Ek+Eg=Ek+Eg

Answer 1

The problem gives us the following situation:

In this type of problem, we can use the theorem of conservation of energy. This tells us that the total energy on the system does not vary, although the for in which it is stored inside the system may vary. If we write the equation for this system we get:

$E=E_k+E_g$

On the first hill, our energy will be:

$E_k+E_g=\frac{mv^2}{2}+mgh=\frac{337*2.7^2}{2}+337*9.8*12=40859.565J$

Thus, our energy on the system is 40859.565J. With this, we can find out how it is distributed in the second hill:

$40859.565=\frac{337*5.5^2}{2}+337*9.8*x$

Then, we can isolate x:

$x=\frac{(40859.565-\frac{337*5.5^2}{2})}{337*9.8}=10.829m$

Then, our height is x=10.829m