Mosquito being charged by dinosaur

[chris097]

Homework Statement

A small mosquito is hovering in the air when a fast and massive dinosaur charges right into it with a speed of 2.62 m/s. If the collision is elastic what is the speed of the mosquito when it bounces off of the dinosaur.

Homework Equations

momentum equation

The Attempt at a Solution

Well since the don't specify the masses I just assume a tiny mass being hit by a massive one. The horizontal speed of the mosquito is 0 and the speed of the dinosaur is 2.62 m/s. I thought it would just be the same speed of the dinosaur (or slightlyyy larger) but this is wrong. Can someone please help?

Thank you very much

 

[redargon]

what equations did you use?

 

[tomcue]

for your question. I would approach this scenario by first examining the physical properties and laws involved. The collision between the mosquito and the dinosaur can be analyzed using the principle of conservation of momentum, which states that the total momentum of the system before and after the collision remains constant.

In this case, the initial momentum of the system is zero since the mosquito is stationary. After the collision, the total momentum of the system should still be zero, since the dinosaur's momentum is in one direction and the mosquito's should be in the opposite direction. This means that the momentum of the mosquito after the collision should be equal in magnitude but opposite in direction to the momentum of the dinosaur.

Using the momentum equation, we can calculate the momentum of the dinosaur before the collision as:

Pd = md * vd

Where Pd is the momentum of the dinosaur, md is its mass, and vd is its velocity.

Since the mosquito is much smaller, we can assume that its mass is negligible compared to the dinosaur's mass. Therefore, the momentum of the mosquito after the collision can be approximated as:

Pm = -Pd = -md * vd

Where Pm is the momentum of the mosquito and -Pd indicates that the momentum is in the opposite direction.

Finally, we can use the same equation to calculate the velocity of the mosquito after the collision:

vm = Pm / mm = -Pd / mm = -md * vd / mm

Where vm is the velocity of the mosquito and mm is its mass.

As you can see, the final velocity of the mosquito after the collision is dependent on the mass of the mosquito. If we assume that the mosquito's mass is very small compared to the dinosaur's, we can see that the final velocity of the mosquito will be very close to the initial velocity of the dinosaur (2.62 m/s in this case). However, if the mosquito's mass is not negligible, then the final velocity of the mosquito will be smaller than the initial velocity of the dinosaur.

In conclusion, the final velocity of the mosquito after the elastic collision with the dinosaur will depend on the mass of the mosquito and will be in the opposite direction of the dinosaur's initial velocity. I hope this helps to clarify the situation.