Question

A 67-kilogram cannon fires a 1 kilogram cannonball at 45 m/sec. If the cannon is on wheels, at what speed does it move backward?

Answer 1

Answer:

-1.4 m/sec  [backwards]

Step-by-step explanation:

The energy of the cannon moving should be equal to the energy contained in the cannonball.  Kinetic energy for each is calculated using KE = (1/2)m$v^{2}$

Let x be the speed of the cannon.

Cannonball:  

KE = (1/2)m$v^{2}$

KE = (1/2)(1kg)(45 m/sec)^2

KE = 22.5   kg*m/sec^2

Cannon:      [The cannon will have the reverse energy]

KE = - (1/2)m$v^{2}$

22.5 kg*m/sec^2 = -(1/2)(67 kg)x^2

22.5 kg*m/sec^2 = -(33.5 kg)x^2

x^2 = (33.5 kg)/(22.5 kg*m/sec^2)

x^2 = -1.4 m/sec  [backwards]