A rocket motor is used to accelerate a kinetic energy weapon to a speed of 1.8 k

Question

A rocket motor is used to accelerate a kinetic energy weapon to a speed of 1.8 km/s in horizontal flight. The exit stream leaves the nozzle axially and at atmospheric pressure with a speed of 3000 m/s relative to the rocket. The rocket motor ignites upon release of the weapon from an aircraft flying horizontally at U0 = 300 m/s. Neglecting air resistance, obtain an algebraic expression for the speed reached by the weapon in level flight. Determine the minimum fraction of the initial mass of the weapon that must be fuel to accomplish the desired acceleration.

Explanation / Answer

From rocket equation
dv = ve*ln(mo/mf)

for the given problem
speed of aircraft , U = 300 m/s
final speed of projectile, v = 1800 m/s
ve = 3,000 m/s

dv = v - 0 = 1800 m/s
hence
1800 = 3000*ln(mo/mf)
mo/mf = 1.8221188

final speed of the projectile = U + v = 1800 + 300 = 2100 m/s
for the given acceleration
mf/mo = 0.5488

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