When a ball is thrown up vertically with velocity $u,$ it attains a maximum height $H.$ What should be the velocity so that maximum height becomes $2H$?

$A$ body dropped from the top of a tower clears $7/16$ of the total height of the tower in its last second of flight. The time taken by the body to reach the ground is........$s$

$A$ window is $50\,cm$ long. $A$ stone is falling from a height of $40\,cm$ above the window. It crosses the window in

$A$ ball is thrown vertically upward. It has a speed of $10 \; m/s$ when it has reached one-half of its maximum height. How high does the ball rise? (Take $g = 10 \; m/s^2$)

$A$ stone thrown down with a speed $u$ takes a time $t_1$ to reach the ground,while another stone thrown upwards from the same point with the same speed takes time $t_2$. The maximum height the second stone reaches from the ground is

With what velocity should a ball be projected vertically so that the distance covered by it in the $5^{th}$ second is twice the distance it covers in its $6^{th}$ second? (Take $g = 10 \, m/s^2$)