A typical raindrop is much more massive than a mosquito and falling much faster

Question

A typical raindrop is much more massive than a mosquito and falling much faster than a mosquito flies. How does a mos quoit survive the impact? Recent research has found that the collision of a falling raindrop with a mosquito is a perfectly inelastic collision. That is. the mosquito is 'swept up" by the raindrop and ends up travelling along with the raindrop. Once the relative speed between the mosquito and the raindrop is zero, the mosquito is able to detach itself from the drop and fly away. Part A A hovering mosquito is hit by a raindrop that is 50 times as massive and falling at 8.7 m/s. a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately after ward if the collision is perfectly inelastic? Because a raindrop is "soft" and deformable. the collision duration is a relatively long 8.0 ms. What is the mosquito's average acceleration, in gs. during the collision? The peak acceleration is roughly twice the value you found, but the mosquito's rigid exoskeleton allows it to survive accelerations of this magnitude. In contrast, humans cannot survive an acceleration of more than about 10 g. At the county fair. Chris throws a 0.15 kg baseball at a 2.5 kg wooden milk bottle, hoping to knock it off its stand and win a prize. The ball bounces straight back at 30 % of its incoming speed, knocking the bottle straight forward. What is the bottle's speed, as a percentage of the ball's incoming speed?

Explanation / Answer

MU = (M + m)V; where M = 50 m, U = 8.7 m/s, find V = ?. V = (50/51)*8.7 = 8.5 m/s ANS. A.

F = m dV/dT = m 8.5/8E-3 = m 1062.5; so G = 1062.5/9.8 = 108.41 G's. ANS. B.

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First you set up your masses

m1= 0.15 kg Ball
m2= 2.5 kg Wooden Bottle

you set up your equation

Initial=Final ( no impulse going on) Initial is the left side and Final the right side

m1v1+m2v2= - m1v1+m2v2 (negative the final m1v1 because it goes contrary as it bounces back)

Your equation should look:
0.15kg(v1)+0 (bottle was on rest)= -0.15(0.3)v1+ 2.5kgv2
0.15kgv1 + 0.045v1=2.5kgV2
0.195V1=2.5kgV2
0.078=(v2/v1)

Multiply by 100 since they are asking for percentage and you should get 7.8%

Note you use (0.3) because it is the percentage 30/100=0.3

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