A missile launcher, mass M , on a horizontal track fires a missile, mass m , hor

Question

A missile launcher, mass M, on a horizontal track fires a missile, mass m, horizontally. To stop the recoil of the launcher, it rolls smoothly (and without friction) up an inclined plane and comes to a stop h meters above ground level. (a) What is the launch speed, vo, of the missile in terms of M, m, h, and g? (The launcher goes from ground level to the incline with no loss in momentum) (b) If the missile launcher%u2019s mass is 4400 kg, the missile%u2019s mass is 110 kg, and the final height of launcher is 4.0 m. Find missile launch speed.

Explanation / Answer

according to law conservation of momentum

M*v = m*vo

if the launcher reaches h height

v = sqrt(2*g*h)

vo = M*sqrt(2*g*h)/m

b)v0 = 4400*sqrt(2*9.8*4)/110 = 354.17 m/s

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