$A$ man of height $2 \ m$ walks at a uniform speed of $5 \ km/hr$ away from a lamp post which is $6 \ m$ high. Find the rate at which the length of his shadow increases in $km/hr$.

$A$ stone is dropped into a pond. Waves in the form of circles are generated and the radius of the outermost ripple increases at the rate of $5 \ cm/sec$. The rate at which the area increases after $2 \ seconds$ is:

$A$ ladder $5 \ m$ long rests against a vertical wall. If its top slides downwards at the rate of $10 \ cm/sec$,then the foot of the ladder is sliding at the rate of . . . . . . $m/sec$,when it is $4 \ m$ away from the wall.

$A$ ball thrown vertically upwards falls back on the ground after $6 \, s$. Assuming that the equation of motion is of the form $s = ut - 4.9t^2$,where $s$ is in metres and $t$ is in seconds,find the initial velocity $u$ at $t = 0$ in $m/s$.

$A$ kite is $120 \ m$ high and $130 \ m$ of string is out. If the kite is moving away horizontally at the rate of $39 \ m/sec$,then the rate at which the string is being paid out is:

Find the rate of change of the area of a circle with respect to its radius $r$ when $r = 3 \text{ cm}$. (in $\pi \text{ cm}$)