Question

can someone show me how to do intergral in respect to t, for velocity final = squaroot of 2gh?

v = (2gh)^(1/2)

Answer 1

This above formula can be derived by using the conservation of energy. This is the velocity when the complete potential energy of the system is converted to its kinetic energy. Hence we can write,

Let us take the initial velocity of the ball be zero. After moving a distance dx above the Earth we can write, the energy equation as,

By conservation of energy we can say that,

The integration limits are from 0 to h. Hence we will get the equation as,