- 9

- 0

**1. Homework Statement**

A frictionless path is set up between two points in space at different heights, such that a body released from the higher point along this path takes minimum possible time to reach the lower point. Show that the path is a cycloid. Also show that a body released along this path takes about 25% lesser time as compared to travelling along a straight path.

**2. Homework Equations**

Energy conservation,

**3. The Attempt at a Solution**

Let us assume that the total height difference is H and the horizontal distance is X.

when the body falls through a height y its speed is [tex]\sqrt{2gy}[/tex]

[tex]\frac{dx}{dt}[/tex]= vcos[tex]\theta[/tex]

[tex]\frac{dy}{dt}[/tex]= vsin[tex]\theta[/tex]

i am unable to integrate and apply the condition for minimum time- please help.