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 highway (point M ) as shown in the 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?

Step-by-step solution

Let the car turn of the highway at a distance ' x ' from the point M . So, RM =x And if speed of car in field is v , then time taken by the car to cover the distance Q R=Q M-x on the highway, t₁= Q M-x 2 v Time taken to travel the distance ' R P^ in the field t₂= d^2+x^2 v Total time elapsed to move the car from Q to P t=t₁+t₂= Q M-x 2 v + d^2+x^2 v or x= d 2^2-1 = d 3