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.

Explanation:

From the L;aw of conservation of momentum

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

$(m \times 0) + (45 \times 8.4) = [m +45m]v$

$378m = [46m] \times v$

$378 = 46\times v$

$V = \frac{378}{46}$

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,

$F = m \times \frac{dv}{dt}$

$F = m \times \frac{8.22}{8.0 \times 10^{-3}}$

$F = 1.028 \times 10^3m$--------------------(1)

Force due to gravity,

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

Comparing both the equations  (1) and (2)

$g = 1.028 \times 10^3$

$a_{avg} = \frac{1.028 \times 10^3}{9.8}$

=105 g

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