Question

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).

Answer 1

Answer:

The new velocity of the military airplane will be equal to 27.2 m/s.

Explanation:

Initial mass of the plane = m₁ = 7800 kg

Initial Velocity of the plane = v₁ = 30 m/s

Mass of the plane after refueling = m₂ = 7800 + 800 = 8600 kg

New velocity = v₂ = ?

According to the law of conservation of momentum, the momentum of an object must stay the same. So, if we are increasing the mass of the object, its velocity must decrease. According to the law of conservation of momentum:

$m_{1}v_{1}=m_{2}v_{2}$

Substituting the values, we get:

$7800(30)=8600(v_{2})\\\\ v_{2}=27.2m/s$

Thus, the new velocity of the plane would be 27.2 m/s

Answer 2

Answer:

$V_2=27.2m/s$

Explanation:

using the conservation of the linear momentum:

$P_i = P_f$

so:

$M_1V_1 = M_2V_2$

where $M_1$ is the mass of the plane, $V_1$ the initial velocity of the plane, $M_2$ the new mass of the plane and $V_2$ the new velocity of the plane.

Replacing values, we get:

$(7800kg)(30m/s)=(7800kg+800kg)V_2$

Solving for $V_2$:

$V_2=27.2m/s$