# Sliding down the curved/straight slide

1. Mar 13, 2015

### cloveryeah

1. The problem statement, all variables and given/known data
a boy is sliding down a curved slide, another boy with same mass is sliding down a straight slide. if both slides have the same height, which of them will reach the bottom first?
2. Relevant equations

3. The attempt at a solution
i m thinking if it is related to 1/2 mv^2 = mgh
and final v will be the same in both cases
but how can i calculate the time required?

2. Mar 13, 2015

### Suraj M

if the final velocity is not the same, speed is the same
one has a larger distance to cover, so it would take a different time to reach the ground.
"Even though it is longer than the other tracks, the curved slide is the quickest. This is because it is much steeper at the beginning, which means that gravity has a greater effect on the ball causing it to accelerate more quickly and reach its top speed sooner."
Also, what if the curve of the slide is a brachistochrone curve?
see this, it has the total explanation :http://www.qedcat.com/misc/94.html

Last edited: Mar 13, 2015
3. Mar 13, 2015

### haruspex

In case it's not clear from Suraj's reply, there's not enough information. It depends on the details of the curve. However, there are some simple assumptions that can be made which allow an answer. For a start, it is obvious that if the curved slide starts off descending more slowly than the straight slide it can take longer, so assume that for any given horizontal distance from the start the curved slide is no higher than the straight slide.

Last edited: Mar 13, 2015