Question

A missile of mass 1.25*10^2 kg is fired from a plane of mass 4.65*10^3 kg initially moving at a speed of 2.95*10^2 m/s. If the speed of the missile relative to the plane is 1.11*10^3 m/s, what is the final velocity of the plane?

Answer 1

Given that:

Mass of missile, m1 = 1.25*10^2 kg

Mass of plane, m2 = 4.65*10^3 kg

total mass of missile + plane, M = 1.25*10^2 + 4.65*10^3 = 4.775*10^3 kg

Initial speed of missile + plane, U = 2.95*10^2 m/s

V1 = final speed of missile = ?

V2 = final speed of plane = ?

final speed of missile relative to plane = V_mp = V1 - V2 = 1.11*10^3 m/s

V1 = V2 + 1.11*10^3

Using momentum conservation:

Pi = Pf

M*U = m1*V1 + m2*V2

4.775*10^3*2.95*10^2 = 1.25*10^2*(V2 + 1.11*10^3) + 4.65*10^3*V2

V2 = (4.775*10^3*2.95*10^2 - 1.25*10^2*1.11*10^3)/(1.25*10^2 + 4.65*10^3)

V2 = 265.94 m/s

V2 = final velocity of the plane = 2.66*10^2 m/s

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