A piece of stone is dropped from the top of a pillar. It travels the last h ft of the height in t s. Prove that the time of fall for the stone is `((t)/(2)+(h)/("gt"))`s.

A stone is dropped from the top of a vertical pillar. When the stone has fallen through a height x, another stone is dropped from height y below the top of the pillar. Both the stones touch the ground at the same time . Prove that the height of the pillar should (x+y)^(2)/(4x) .

A stone is dropped from a height of 19.6m. What is the time taken by the stone to travel the last metre of the path?

A balloon is rising upwards from rest with acceleration (g)/(8) . A stone is dropped from the balloon when it is at height H. Show that the time by which the stone will touch the ground is 2 sqrt((H)/(g)) .

A piece of stone is dropped from the top of a tower 90 m tall and at the same time another piece of stone is thrown upwards with a velocity of 30 "m.s"^(-1) from the base of the tower. When and where will the stone pieces meet?

A balloon at rest on the ground is rising upward with acceleration (g)/(8) . A stone is dropped from the balloon when it is at height H. Show that the time taken by the stone to touch the ground is 1/2 sqrt((H)/(g)) .

At a distance 2h m from the foot of a tower of height h m the top of the tower and a pole at the top of the tower subtend equal angles. Prove that the height of the pole should be (5h)/(3) m.

From the bottom of a pole of height h the angle of elevation of the top of a tower is alpha and the pole subtends an angle beta at the top of the tower . Prove that the height of the tower is (h cot(alpha - beta))/(cot(alpha - beta) - cot alpha) .

A piece of stone was dropped from a stationary baloon. The stone covered 13.9 m during the last (1)/(7) s of its descent. Find the height of the balloon and the velocity of the stone whe it strikes the ground. [g = 9.8 "m.s" ^(-2) ]