A $750 g$ peregrine falcon dives straight down towards a $400 g$ pigeon, which is flying level to the ground. Just before the falcon makes impact its velocity is $35 m / s$ . The velocity of the falcon and the pigeon in its talons immediately after impact is most nearly

35 m / s

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31.95 m / s

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28.9 m / s

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25.85 m / s

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22.8 m / s

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Solution

The correct option is E $22.8 m / s$
Since after the impact, the falcon and pigeon move together and there is no external force acting on the system(falcon and pigeon),
$m_{f a l c o n} u = (m_{f a l c o n} + m_{p i g e o n}) v$
$⟹ v = \frac{m_{f a l c o n}}{m_{f a l c o n} + m_{p i g e o n}} u$
$= \frac{750}{750 + 400} \times 35 m / s = 22.8 m / s$

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