Question

A bully is spraying water at some future engineer on the playground. The nerd has three trash can lids around to choose from to block the water with. Lid #1 curls the water around and directs the flow back at the bully (but he/she is too far to be hit by the flow). Lid #2 is completely flat the water sprays up and down. Lid #3 has been punched “in” and it flows the water above the nerds head at an angle 45 degrees from impinging flow. Using the principles of conservation of momentum, help the nerd select the lid which requires the least amount of force to restrain the water (he/she is pretty weak).

Answer 1

The least amount of force to restrain the water will be when the change in momentum along the direction of the water after reflection is the least.

In the first case, the change in momentum along the water direction is double the initial momentum

[since v = - u]

so, by conservation of momentum, the recoil velocity of the kid will be large hence the force will be large.

In the third case, the change in momentum is along the direction of water is small

[v = - u cos45]

and so the force will be smaller compared to the 1st case.

In the second case, all the linear momentum along the direction of motion of water gets converted to momentum perpendicular to the direction of motion of water. Therefore, by conservation of momentum, the recoil velocity will be least and hence it will require the least amount of force.