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 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…

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 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?

Accepted Answer

(2) d/(√3). Let RM = x and QM = L. On the highway he covers L - x at speed v; in the field he covers RP = √x² + d² at speed v/2. T = (L - x)/v + (2√x² + d²)/v. (dT)/(dx) = -1/v + (2x)/(v√x² + d²) = 0 ⇒ 2x = √x² + d². 4x² = x² + d² ⇒ x = d/(√3).

Step-by-step solution

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