Three different objects of masses ${m_1},{m_2}$ and ${m_3}$ are allowed to fall from rest and from the same point $‘O’$ along three different frictionless paths. The speeds of the three objects, on reaching the ground, will be in the ratio of

A man is standing on top of a building $100\, m$ high. He throws two balls vertically, one at $t = 0$ and after a time interval (less than $2\,\sec $). The later ball is thrown at a velocity of half the first. The vertical gap between first and second ball is $+15\, m$ at $t = 2\,\sec $. The gap is found to remain constant. Calculate the velocity with which the balls were thrown and the exact time interval between their throw.

A ball is dropped downwards. After $1$ second another ball is dropped downwards from the same point. What is the distance between them after $3\, seconds$………..$m$

A ball is dropped from a bridge of $122.5$ metre above a river. After the ball has been falling for two seconds, a second ball is thrown straight down after it. Initial velocity of second ball so that both hit the water at the same time is …… $m / s$

Water drops are falling from a nozzle of a shower onto the floor, from a height of $9.8\, {m}$. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.  (In $m$)