Question

A bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has speed of $ 27 \,km\, h^{-1} $ while the other has the speed of $ 18 \,km \,h^{-1} $ . The bird starts moving from first car towards the other and is moving with the speed of $ 36\, km \,h^{-1} $ when the two cars were separated by $ 36 \,km $ . The total distance covered by the bird is

• A. $ 28.8\,km $
• B. $ 38.8\,km $
• C. $ 48.8\,km $
• D. $ 58.8\,km $

Answer 1

Answer: (A)

Velocity of car $ A $ , $ v_A = + 27\, km \,h^{-1} $
Velocity of car $ B $ , $ v_B = -18 \,km \,h^{-1} $
Relative velocity of car $ A $ with respect to car $ B $
$ =v_{A}-v_{B}+27\,km\,h^{-1}-\left(-18\,km\,h^{-1}\right)=45\,km\,h^{-1} $
Time taken by the two cars to meet $ =\frac{36\,km}{45\,km\,h^{-1}}=0.8\,h $
Thus, distance covered by the bird
$ = 36\, km\, h^{-1} \times 0.8\, h = 28.8 \,km $