A hovering mosquito is hit by a raindrop that is 45 times as massive and falling at 8.2 m/s , a typical raindrop speed. How fast is the raindrop, with the attached mosquito, falling immediately afterward if the collision is perfectly inelastic

The speed of the raindrop  and the mosquito is 8.02 m/s.

Explanation:

mass of mosquito = m

mass of drop = 45 m

initial velocity of mosquito, u = 0 m/s  

initial velocity of drop,  u' = 8.2 m/s

During the inelastic collision, the momentum of the system is conserved.  

Let the speed of rain drop and the mosquito is v.

Use the conservation of momentum

m x u + 45 m x u' = (m +  45 m) v

m x 0 + 45 m x 8.2 = 46 m x v

v = 8.02 m/s

conduction, convection, radiation

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.