$A$ ball of mass $0.5 \; kg$ is dropped from a height of $10 \; m$. The height from the ground,at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity,is $\dots \; m$. (Use $g = 10 \; m/s^2$).

$A$ 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 $m/s$)?

$A$ ball is thrown straight upward from the ground with a speed of $20 \,m/s$. The ball is caught on its way down at a point $5 \,m$ above the ground. The time taken by the ball during the entire trip is (assume $g = 10 \,m/s^2$):

$A$ 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 $......... \, m/s$.

$A$ stone dropped from the top of a tower is found to travel $\left(\frac{5}{9}\right)$ of the height of the tower during the last second of its fall. The time of fall is ....... $s$.

$A$ stone is thrown vertically up from the top end of a window of height $1.8 \,m$ with a velocity of $8 \,m/s$. The time taken by the stone to cross the window during its downward journey is (Acceleration due to gravity $= 10 \,m/s^2$) (in $\,s$)