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

$A$ stone is dropped from the top of a tower of height $h = 60 \ m$. Simultaneously,another stone is projected vertically upwards from the foot of the tower. They meet at a height $\frac{2h}{3}$ from the ground level. Find the initial velocity of the stone projected upwards. (Take $g = 10 \ ms^{-2}$) (in $ms^{-1}$)

$A$ ball is dropped from a bridge of $122.5 \ m$ above a river. After the ball has been falling for $2 \ s$,a second ball is thrown straight down after it. What is the initial velocity of the second ball so that both hit the water at the same time (in $m/s$)?

$A$ boy standing at the top of a tower of $20 \, m$ height drops a stone. Assuming $g = 10 \, m/s^2$,the velocity with which it hits the ground is ......... $m/s$.

$A$ body projected vertically upwards with a velocity $u$ returns to the starting point in $4 \, s$. If $g = 10 \, m/s^2$,the value of $u$ is $......... \, m/s$.

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{th} \, s$ after its fall and the next droplet is $34.3 \, m$. At what rate are the droplets coming from the tap? (Take $g = 9.8 \, m/s^2$)