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
Let x be the speed of the cannon.
<u>Cannonball: </u>
KE = (1/2)m
KE = (1/2)(1kg)(45 m/sec)^2
KE = 22.5 kg*m/sec^2
<u>Cannon:</u> [The cannon will have the reverse energy]
KE = - (1/2)m
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]