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Calculate the momentum of a 1,500 kg car traveling at 6 m/s.
A military airplane sometimes needs to refuel in mid-air, and another plane flies above it to add the fuel. If a plane with a mass of 7,800 kg is traveling with a velocity of 30 m/s and refuels by adding an additional 800 kg of jet fuel, what will its new velocity be? (Hint: This is a multi-step problem).

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Answer:

See the answers below.

Explanation:

Momentum is defined as the product of mass by velocity, in this way we have the following equation.

[tex]P=m*v[/tex]

where:

P = momemtum [kg*m/s]

m = mass = 1500 [kg]

v = velocity = 6 [m/s]

[tex]P = 1500*6\\P=9000 [kg*m/s][/tex]

Now we have to calculate the momentum of the plane when it travels at 30 [m/s].

[tex]P_{airplane}=m_{plane}*v_{plane}\\P_{airplane}=7800*30\\P_{airplane}=234000[kg*m/s][/tex]

Now this same momentum must be conserved, in such a way that the mass is increased but the velocity must decrease for the momentum to be conserved.

[tex]P=m_{new}*v_{new}\\234000=(7800+800)*v_{new}\\234000=8600*v_{new}\\v_{new}=27.2[m/s][/tex]

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