$A$ juggler maintains four balls in vertically upward motion. He throws the next ball every $1/4 \, s$. For the show to continue,what should be the height to which he throws each ball? (Assume $g = 10 \, m/s^2$)

$A$ ball projected vertically upwards with a velocity '$v$' passes through a point $P$ in its upward journey in a time of '$x$' seconds. From there,the time in which the ball again passes through the same point $P$ is

Two balls $A$ and $B$ are placed at the top of a $180 \,m$ tall tower. Ball $A$ is released from the top at $t = 0 \,s$. Ball $B$ is thrown vertically downward with an initial velocity $u$ at $t = 2 \,s$. Both balls meet at a point $100 \,m$ above the ground. Find the value of $u$ in $m \,s^{-1}$. [Use $g = 10 \,m \,s^{-2}$]

$A$ body falls freely for $10 \ s$. What is its average velocity during this journey (in $m/s$)? (Take $g = 10 \ m/s^2$)

From the top of a $64\, ft$ high tower,a stone is thrown upwards vertically with the velocity of $48\, ft/s$. The greatest height (in $ft$) attained by the stone,assuming the value of the gravitational acceleration $g = 32\, ft/s^2$,is

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?