Question

A hovering mosquito is hit by a raindrop that is 30 times as massive and falling at 8.1 m/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic?

Answer 1

Answer on Question #63131, Physics / Mechanics

A hovering mosquito is hit by a raindrop that is 30 times as massive and falling at $8.1 \, \text{m/s}$, a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic?

Solution

According to the conservation of momentum,

$$m _ {m} v _ {m} + m _ {d} v _ {d} = \left(m _ {m} + m _ {d}\right) v;$$ $$v = \frac {m _ {m} v _ {m} + m _ {d} v _ {d}}{\left(m _ {m} + m _ {d}\right)};$$ $$v = \frac {m \times 0 + (30m) \times 8.1}{(m + 30m)} = \frac {243m}{31m} = 7.84 \, \text{m/s}$$

Answer: $7.84 \, \text{m/s}$

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