Question

Two cars intially at 20 km from the square are approaching towards it. One at 60 km/h and another at 80 km/h. Minimum separation between the cars is [in km] (Write until two digits after the decimal point.)

Solution

Place the frame of reference on B, VAB=VA−VB=80^j−60^i then the path of A is as shown by the dotted line in the figure. Angle made by path is 37 degrees.  The perpendicular x becomes the shortest distance between A and B. b20=tan 37∘ ⇒b=20×34=15 ⇒a=20−15=5 ⇒x=a cos 37=5×45=4

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