Question

A jet of water of cross-sectional area A hits a plate normally with velocity v.the plate is moving in the direction of the jet with velocity V.therefore the force exerted on the plate is proportional to

a). (v-V)
b). (v-V)²​

Answer 1

The force exerted on a plate by a jet of water is proportional to the square of the relative velocity of the water jet and the plate, which is (v-V)², where v is the velocity of the jet and V is the velocity of the plate.

Step-by-step explanation:

The force exerted by a jet of water hitting a plate normally depends on the relative velocity of the water and the plate. The force is linked to the change in momentum that occurs when the jet hits the plate and comes to a stop. This change in momentum, and therefore the force, is proportional to the mass flow rate (the amount of mass hitting the plate per unit time) multiplied by the change in velocity of the water jet relative to the plate.

If the plate is moving with velocity V in the direction of the water jet, which has a velocity v, the relative velocity between the water and the plate is (v-V).

The mass flow rate is equal to the density times the cross-sectional area A times the relative velocity (v-V). Therefore, since force is proportional to the product of mass flow rate and the relative velocity, we find that the force exerted on the plate is proportional to the square of the relative velocity, i.e., (v-V)², assuming constant density.