$A$ ball is projected vertically upward with an initial velocity of $50 \; ms^{-1}$ at $t = 0 \; s$. At $t = 2 \; s$,another ball is projected vertically upward with the same velocity. At $t = \dots \; s$,the second ball will meet the first ball $(g = 10 \; ms^{-2})$.

$A$ particle is released from rest from a tower of height $3h$. The ratio of times taken to fall through successive equal heights $h$,i.e.,$t_1 : t_2 : t_3$ is

$A$ stone is thrown with an initial speed of $4.9 \, m/s$ from a bridge in a vertically upward direction. It falls down into the water after $2 \, s$. The height of the bridge is .......... $m$.

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 $g = 10 \, m/s^2$)

Reaction time: When a situation demands our immediate action,it takes some time before we really respond. Reaction time is the time a person takes to observe,think,and act. For example,if a person is driving and suddenly a boy appears on the road,then the time elapsed before he slams the brakes of the car is the reaction time. Reaction time depends on the complexity of the situation and on an individual.
You can measure your reaction time by a simple experiment. Take a ruler and ask your friend to drop it vertically through the gap between your thumb and forefinger. After you catch it,find the distance $d$ travelled by the ruler. In a particular case,$d$ was found to be $21.0 \; cm$. Estimate the reaction time in seconds. (in $; s$)

What is the ratio of the distances covered by a freely falling body in the $1^{st}$,$2^{nd}$,and $3^{rd}$ seconds of its motion?