91Ó°ÊÓ

The given data can be listed below as-

• The mass of the car is $2045 kg.$
• The car is moving at a speed of $29 m/s.$
• The mass of the mosquito is$0.0025 kg.$

This law illustrates that the total momentum of a body before and after the collision becomes equal if no external forces get involved.

The gravitational law states that the force exerted on a body is directly proportional to the product of the masses and inversely proportional to the square of the distances amongst them.

The equation of the momentum of a body gives the momentum change of the car and truck and the reason for which the collision is much more damaging to the mosquito.

The equation of the force exerted on a body gives the magnitude of the force exerted on the car by the mosquito.

a) From the law of conservation of momentum, the equation of the momentum change of the mosquito can be expressed as-

$p_1=m\mathrm{Δ}v$

Here, $p_1$is the momentum change of the mosquito, m is the mass of the mosquito and $\mathrm{Δ}v$is the change of the velocity of the mosquito that is $29 \mathrm{m}/\mathrm{s}-0 \mathrm{m}/\mathrm{s}=29 \mathrm{m}/\mathrm{s}$.

Substituting the values in the above equation, we get-

role="math" localid="1658207903297" $$\begin{gathered} p=(0.0025 kg)×(29 m/s-0 m/s=29m/s) \\ p=0.0725 kg.m/s \end{gathered}$$

Thus, the approximate momentum change of the mosquito is$0.0725 kg.m/s$and it is in the positive direction.

b) As the force exerted by the car is F that can be expressed as-

$F=G\frac{m_{\text{car}}\text{?}{m}_{\text{mosquito}}}{r^2}$

Here, r is the distance between the car and the mosquito$m_{\text{car}}and{m}_{\text{mosquito}}$

masses of the car and the mosquito respectively.

the magnitude of the force exerted on the car by the mosquito is expressed as:

$F=G\frac{m_{\text{mosquito}}\left[m_{car}\right]}{r^2}$

Thus, the magnitude of the force exerted on the car by the mosquito is also F.

c) According to the law of conservation of momentum, the momentum change of the car is the same as the momentum change of the mosquito.

Thus, the approximate momentum change of the car is$0.0725 kg.m/s$ and it is in the positive direction.

d) Since time duration of the collision is negligible but the change in the momentum of the mosquito is big, that is the main reason the collision is much more damaging to the mosquito than to the car.

Thus, the collision is much more damaging to the mosquito than to the car as the change in the momentum of the mosquito is big.