A cannon of mass 550 103 kg is rigidly bolted to the earth s

A cannon of mass 5.50 103 kg is rigidly bolted to the earth so it can recoil only by a negligible amount. The cannon fires an 90.0-kg shell horizontally with an initial velocity of +595 m/s. Suppose the cannon is then unbolted from the earth, and no external force hinders its recoil. What would be the velocity of an identical shell fired by this loose cannon? (Hint: In both cases assume that the burning gunpowder imparts the same kinetic energy to the system. Enter your answer to the nearest whole number. Indicate the direction with the sign of your answer.) m/s

Solution

let

M = 5.5*10^3 kg

m = 90 kg

when the canon is bolted the speed of shell, u = 595 m/s

let V is the recoil speed of canon and u\' is the speed of shell when the canon is unbolted.

Apply, conservation of momentum.

0 = M*V + m*u\'

V = m*u\'/M

now Apply conservation of energy

0.5*m*u^2 = 0.5*m*u\'^2 + 0.5*M*V^2

m*u^2 = m*u\'^2 + M*(m*u\'/M)^2

m*u^2 = m*u\'^2 + m^2*u\'^2/M

u^2 = u\'^2 + m*u\'^2/M

u^2 = u\'^2*(1 + m/M)

u\' = u/sqrt(1 + m/M)

= 595/sqrt(1 + 90/(5.5*10^3))

= +590.2 m/s <<<<<<<<-----------------Answer