Question

when a ball is thrown vertically upwards with velocity V0, it reaches maximum height of 'h'. if one wishes to triple the maximum height then the ball should be thrown with what velocity​

Answer 1

Maximum height means final velocity is zero.

Using last equation of motion - v2 = u2 + 2gh

h = 0 - u2/-2g = u^2/2g.

To triple maximum height, we have,

let us take u1 as the new initial velocity

3h = u1^2/2g

3u^2/2g = u1^2/2g

cancel 2g on both sides.

3u^2 = u1^2

hence u1 = root3 u.

That means the first initial velocity should be multiplied by 1.732 to get the new u to throw the ball which will triple max. height.