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Question

Two cars A and B are moving in the same direction along a straight line with speeds $100\text{ }km/h$ and $80\text{ }km/h$, respectively such that car A is moving ahead of car B . A person in car B throws a stone with a speed v so that it hits the car A with a speed of $5\text{ }m/s$. The value of v is

$\_\_\_\_$ km/h.

Options

A.18
B.28
C.38
D.48

Solution

Sol. [Key Concept: Work in B's frame: the stone's ground speed $V_{s} = v + 80$; its approach relative to A is the given $5$ m/s.]

$${V = {\overrightarrow{V}}_{SB} }{V = {\overrightarrow{V}}_{S} - {\overrightarrow{V}}_{B} }{V_{B} + V = {\overrightarrow{V}}_{S} }{{\overrightarrow{V}}_{s} = V + 80 }{{\overrightarrow{V}}_{SA} = 5\text{ }m/s = 18\text{ }km/hr }{{\overrightarrow{V}}_{S} - {\overrightarrow{V}}_{A} = {\overrightarrow{V}}_{SA} }{V + 80 - 100 = 18\text{ }km/hr }{V - 20 = 18 }{V = 38\text{ }km/hr }$$

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