A cat moves uniformly with speed 5 ms-1, so that it is always headed towards a rat is moving on a straight line with constant velocity 3 ms-1. At initial moment, their velocities are perpendicular to each other and they are separated a distance 16 m apart. Find the time (in second) after which cat catches the rat.

The relative velocity of approach of cat to rat at point P is  −dldt=v0−vrcos⁡θ=5−3cos⁡θ⇒ ∫160 −dl=∫0t0 5dt−3∫0t0 cos⁡θdt⇒ 16=5t0−3∫0t0 cos⁡θdt    ......(i)For catching the rat by cat, horizontal distance travelled by both should be same∴     vrt0=∫0t0 vccos⁡θdt Or     3t0=5∫0t0 cos⁡θdt∴     ∫0t0 cos⁡θdt=35t0    .......(ii)From Eqs. (i) and (ii), we get16=5t0−3×35t0=5t0−95t0=165t0∴ t0=5s