Question

The velocity acquired by the body when it falls through a height h is v. If it further travel a distance x what is the change in its velocity

Answer 1

A body is fall from a certain height, velocity at height h , is v.

here, initial velocity of body, u = 0

using formula, v² = u² + 2as

or, v² = 0 + 2gh = 2gh

or, v = √(2gh).....(1)

body further travels a distance x,

then, initial velocity for this situation, u = = √(2gh) , s = x

using formula, v² = u² + 2as

or, v'² = (√2gh)² + 2gx

or, v'² = 2gh + 2gx

or , v' = √{2g(h + x)}

now ,change in velocity = v' - v

= √{2g(h + x)} - √(2gh)

= √(2gh) [ √{(h + x)/h} - 1 ]