Question

A man in a car at location Q on a straight highway is moving with speed v. He decides to reach a point P in a field at a distance d from the highway (Point M) as shown in figure.Speed of the car in the field is half to that on the highway.What should be the distance RM, so that the time taken to reach P is minimum ?

Answer 1

Average speed $=\frac{totaldistancecovered}{totaltimetaken}$

Time taken to travel

from Qto$R=\frac{x}{v}$

Time taken to travel from R to $P=\frac{\sqrt{d^2+{(l-x)}^2}}{v/2}$

Total time$t=\frac{x}{v}+\frac{2.\sqrt{d^2+{(l-x)}^2}}{v}$

$t$ to be min,$\frac{dT}{dx}=0$

$\frac{1}{v}+\frac{2}{v}.\frac{1}{2\sqrt{d^2+{(L-x)}^2}}.-2(L-x)=0$

$L-x=\frac{d}{\sqrt{3}}$