Complete Question
A typical raindrop is much more massive than a mosquito and falling much faster than a mosquito flies. How does a mosquito 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 traveling 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.
A) A hovering mosquito is hit by a raindrop that is 45 times as massive and falling at 8.9m/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic?
B) 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 g's, 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.
Answer:
A. Speed of raindrop = 8.71m/s
B. Mosquito's Average Acceleration = 110.97G
Explanation:
A.
The collision is perfectly inelastic
This occurs when the maximum amount of kinetic energy of a system is lost. In a perfectly inelastic collision and the colliding particles stick together.
A perfect inelastic collusion is given by
MU = (M + m)V;
Where
m = mass of mosquito
M = 45 m,
U = Initial Velocity = 8.9 m/s
V = ?.
Substitute the values, in the above equation.
45m * 8.9 = (45m + m) * V
=> 400.5m = 46m * V ---- Divide through by 46m
=> V = 400.5m/46m
V = 8.70652173913
V = 8.71m/s ----- Approximated
So, the speed of the raindrop after the collision is approximately 8.71m/s
B.
To solve this, we'll make use of
F = m dV/dT
Where dV = raindrop velocity after collision = 8.71m/s
dT = Duration of raindrop = 8.0ms = 8E-3s
Here, we assume that the mass of the mosquito is 1.
So,. F = 1 * 8.71/8E-3
F = 8.71/8E-3
F = 1.08875E3
1 g = 1/9.8
1.08875E3g = 1.08875E3g / 1.8
F = 110.97G
