Question

a 30 kg cart is travelling in a zero friction environment at a constant velocity of 5m/s. It's about to go up a very steep hill. How high will the cart be when the velocity changes to zero? PLEASE HELP

Answer 1

1.27551m

Step-by-step explanation:

This is a simple energy convertion problem. Since there is no friction, and assuming no air drag and other external factors, mechanical energy should be conserved in this system.

Thus, we get:

`KE_(initial) + PE_(initial) = KE_(final) + PE_(final)`

We also know that the gravitational potential energy is equal to mgh, while the KE can be calculated using
`(1)/(2)mv^2`

One thing to note here, is that the final KE will be 0, as there is no velocity at the end. Furthermore, we also can set the initial PE as 0 as we are looking at relative height, and at the start it is at h=0.

`KE_(initial) = PE_(final)`

Plugging in:

`(1)/(2)*30*5^2 = 30*9.8*h`

Solving for h, we get 1.27551m