Collision between moving and stationary object

[Ezio3.1415]

Consider a feral elephant that charges a hovering stationary fly with
a speed of 5m/s at a hovering fly. What is the speed with which the fly will recoil?

Well I know the answer's 10m/s as the mass of the fly is negligible with respect to the mass of the elephant... But how?

 

[mathman]

Since the fly mass is negligible, the center of mass is coincident with the elephant. In the c.m. system (stationary elephant) the fly hits the elephant at 5 m/s, bounces off and recoils at 5 m/s in the opposite direction. Add the c. m. speed and the fly will be going 10 m/s.

 

[Ezio3.1415]

Thank you... :)

 

[sophiecentaur]

I prefer the model of a ball bearing being fired at an oncoming express locomotive with a thick steel plate on the front. Same principle but the resulting high speed ball bearing is somehow a more attractive idea than a squashed fly.

Also, a really useful version of this is the way you can use slingshot orbits around large planets to speed up space vehicles. It's all to do with transfer of momentum.

 

[PJC01]

I can explain the concept of conservation of momentum to understand the speed at which the fly will recoil. According to this principle, in a closed system, the total momentum before and after a collision remains constant. In this situation, the elephant and the fly can be considered as the two objects in the closed system.

Before the collision, the elephant has a momentum of 5m/s (mass of the elephant x velocity) and the fly has a momentum of 0m/s (negligible mass x 0 velocity). Therefore, the total momentum of the system is 5m/s.

After the collision, the elephant will transfer its momentum to the fly, causing it to recoil in the opposite direction. Since the total momentum of the system must remain constant, the fly will have a momentum of 5m/s in the opposite direction.

Using the equation for momentum (p=mv), we can calculate the velocity of the fly after the collision. As the mass of the fly is negligible, we can assume that its final velocity will be equal to the momentum, which is 5m/s in this case.

Therefore, the speed at which the fly will recoil is 5m/s in the opposite direction to the elephant's charge. This is due to the principle of conservation of momentum and the fact that the mass of the fly is negligible compared to the elephant's mass.