$A$ player throws a ball upwards with an initial speed of $29.4\; m s^{-1}$. What are the velocity and acceleration of the ball at the highest point of its motion?

Galileo's law of odd numbers: "The distances traversed, during equal intervals of time, by a body falling from rest, stand to one another in the same ratio as the odd numbers beginning with unity [namely, $1: 3: 5: 7 \ldots$]". Prove it.

$A$ ball is released from the top of a tower of height $h$ meters. It takes $T$ seconds to reach the ground. What is the position of the ball at $T/3$ seconds?

$A$ stone is dropped from a height of $100 \ m$, while another one is projected vertically upwards from the ground with a velocity of $25 \ m/s$ at the same time. The time in seconds after which they will have the same height is (acceleration due to gravity, $g = 10 \ m/s^2$):

$A$ 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 $m$)

$A$ body thrown vertically upwards with an initial velocity $u$ reaches maximum height in $6$ seconds. The ratio of the distances travelled by the body in the first second and the seventh second is