Draw the graph of $y$ versus $t$ for an object falling freely,where $y$ is the vertical displacement and $t$ is time.

$A$ person sitting on the ground floor of a building notices through a window of height $1.5 \; m$ that a ball dropped from the roof of the building crosses the window in $0.1 \; s$. What is the velocity (in $m/s$) of the ball when it is at the topmost point of the window? (Take $g = 10 \; m/s^2$)

$A$ body is projected vertically upward with a velocity of $20 \, m/s$ from the top of a tower of height $200 \, m$. With what velocity will it strike the ground (in $m/s$)? (Take $g = 10 \, m/s^2$)

$A$ person throws balls into the air vertically upward at regular intervals of time of $1 \,s$. The next ball is thrown when the velocity of the ball thrown earlier becomes zero. The height to which the balls rise is (Assume $g = 10 \,m/s^2$) (in $\,m$)

$A$ ball is projected vertically up from the ground. Boy $A$, standing at the window of the first floor of a nearby building, observes that the time interval between the ball crossing him while going up and the ball crossing him while going down is $2 \ s$. Another boy $B$, standing on the second floor, notices the time interval between the ball passing him twice, during up and down motion, is $1 \ s$. Calculate the difference between the vertical positions of boy $B$ and boy $A$. (Assume $g = 10 \ m \ s^{-2}$) (in $m$)

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