Question

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

Answer 1

Question:

Because a raindrop is "soft" and deformable, the collision duration is a relatively long 8.0 ms. How many times larger than gravity is the mosquito's average acceleration during the collision? This is the information I have so far: A hovering mosquito is hit by a raindrop that is 45 times as massive and falling at 8.4 m/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is completely inelastic? V=8.22 m/s

Answer:

The gravity of mosquito is 105 times larger than the raindrop.

Step-by-step explanation:

From the L;aw of conservation of momentum

`m_1u_1 + m_2u_2 = [m_1+m_2]v`

`(m * 0) + (45 * 8.4) = [m +45m]v`

`378m = [46m] * v`

`378 = 46* v`

`V = (378)/(46)`

V= 8.22 m/s

Therefore, the speed of the raindrop attached to the mosquito is 8.22m/s

From the Newton's second law,

`F = m * (dv)/(dt)`

`F = m * (8.22)/(8.0 * 10^(-3))`

`F = 1.028 * 10^3m`--------------------(1)

Force due to gravity,

F =mg -----------------------------------(2)

Comparing both the equations (1) and (2)

`g = 1.028 * 10^3`

`a_(avg) = (1.028 * 10^3)/(9.8)`

=105 g

So, the gravity of mosquito is 105 times larger than the raindrop.