A man in a car at location Q on a straight highway is moving with speed $\mathrm{v}$ . 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?

Question

A man in a car at location Q on a straight highway is moving with speed

\mathrm{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? 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

Quantrex Academy · Accepted Answer

Correct answer: A. d 3

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, t_1= (Q M-x)/(2 v) Time taken to travel the distance ' R P^ in the field t_2= d^2+x^2 v Total time elapsed to move the car from Q to P t=t_1+t_2= (Q M-x)/(2 v)+ d^2+x^2 v or x= d 2^2-1 = d 3

A man in a car at location Q on a straight highway is moving with...

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