State Newton’s second law of motion in terms of momentum.
A toy rocket is made of a water container and compressed air. Compressed air forces water vertically down through a nozzle, and the rocket rises vertically upwards. The nozzle has a circular cross-section of radius $7.5\,\text{mm}$. The density of the water is $1000\,\text{kg m}^{-3}$. Take the water emerging from the nozzle to be a cylinder of radius $7.5\,\text{mm}$ moving at constant speed $13\,\text{m s}^{-1}$ relative to the rocket. Show that the mass of water leaving the nozzle in the first $0.20\,\text{s}$ after launch is $0.46\,\text{kg}$.
Calculate the change in momentum of the water mass in (b)(i) as it exits the nozzle.
Calculate the force exerted by the rocket on this mass of water.
State and explain how Newton’s third law relates to the rocket’s motion caused by the water.
The container has a mass of $0.40\,\text{kg}$. Before launch, the water has an initial mass of $0.70\,\text{kg}$. The mass of the compressed air in the rocket is negligible. Assume that the resistive force on the rocket due to its motion is negligible. At $0.20\,\text{s}$ after launch, show that the total mass of the rocket is $0.64\,\text{kg}$.
Calculate its acceleration.