A revolutionary war cannon, with a mass of 2080 kg, fires a 23.5 kg ball horizon

Question

A revolutionary war cannon, with a mass of 2080 kg, fires a 23.5 kg ball horizontally. The cannonball has a speed of 130 m/s after it has left the barrel. The cannon carriage is on a flat platform and is free to roll horizontally.

What is the speed of the cannon immediately after it was fired?

Answer in units of m/s.

The same explosive charge is used, so the total energy of the cannon plus cannonball system remains the same.

Disregarding friction, how much faster would the ball travel if the cannon were mounted rigidly and all other parameters remained the same?

Answer in units of m/s.

Explanation / Answer

here,

mass of canon , M = 2080 kg

mass of ball , m = 23.5 kg

speed of canon, u = 130 m/s

let the speed of cannon is v m/s

Using conservation of momentum ,

M*v - m * u = 0

2080 * v - 23.5 * 130 = 0

v = 1.47 m/s

the speed of canon immediately after it is fired is 1.47 m/s

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Now, ,let the velocity of cannon ball is u m/s

Using same kinetic energy ,

0.5 * 23.5 * u^2 = 0.5 * 2080 * 1.47^2 + 0.5 * 23.5 * 130^2

solving for u

u = 130.73 m/s
the increase in speed of canon ball is 0.73 m/s

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