Question

With what minimum speed v must a small ball should be pushed inside a smooth vertical tube from a height h so that it may reach the top of the tube? radius of the tube is r. (assume radius of cross-section of tube is negligible in comparison to r)

Answer 1

1/2mv^2=mgh
1/2v^2=gh
$v = \sqrt{2gh}$

Answer 2

${u}^{2} = {v }^{2} + 2as \\ 0 = {v}^{2} - 2gh \\ v = \sqrt{2gh}$