Question

A police inspector in a jeep is chasing a pickpocket on a straight road.the jeep is going at its max speed 'v'(assumed uniform).the pickpocket rides on the motorcycle of a waiting friend when the jeep is at a distance'd' away and the motorcycle starts with acceleration'a' show that the pickpocket will be caught of (v greater than or equal to √2ad

Answer 1

it's the answer is want

Answer 2

If $\bold{v^{2} \geq 2 a d}$ or t is real then the pickpocket will be caught.

Solution:

Let us assume the pick pocket is caught in time “t” and the distance travelled by his bike before getting caught is $S_1$ (which is also the total distance)

Now applying second law of motion

$\begin{array}{l}{S_{1}=u t+\frac{1}{2} a t^{2}} \\ {S_{1}=\frac{1}{2} a t^{2}\{\text {since } u=0\}}\end{array}$

Now during the time in which jeep starts

$\begin{array}{l}{S_{2}=v t-d} \\ {S_{1}-S_{2}=\frac{1}{2} a t^{2}-(v t-d)}\end{array}$

$0=\frac{1}{2} a t^{2}-v t+d$

$t=v+\sqrt{v^{2}-2 a d} \text { or } v-\sqrt{v^{2}-2 a d}$

So, pickpocket will be caught if $\bold{v^{2} \geq 2 a d}$ or t is real.