A water jet pack has lifted a person vertically upwards, as shown in the sketch. He is now stationary at a constant height. Water rises through the tube and is ejected at a speed of 15 m s –1 through two nozzles. In a time of 12 s, each of the nozzles ejects 400 kg of water vertically downwards. What is the momentum of the water ejected by each nozzle in 12 s, and what is the upward force due to the water ejected by the jet pack?

Answer:

23) A

Momentum = mass x velocity = 400 x 15 = 6000 kg m/s
The water ejected achieves a velocity of 15 m/s in 12 seconds.
Initial velocity = 0 m/s
Final velocity = 15 m/s
Acceleration = (final velocity – initial velocity) ÷ time = (15 – 0) ÷ 12 = 1.25 m/s2

Each nozzle ejects 400 kg of water. Two nozzles eject 800 kg.
Force = mass x acceleration
Force = 800 x 1.25 = 1000 N