A cat (including armor, so he isn't hurt by this) is launched at at an unsuspecting enemy. The enemy has a mass of . Assuming a conservation of energy, with the cat retaining no energy, at what speed is the enemy bowled over? (Use units of and round to the nearest hundredth.)
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Remember that the energy of a moving object, with some mass m and some velocity v , is 2 m v 2 . Therefore, the energy of the cat is 2 9 ⋅ 7 0 2 or 2 9 ⋅ 4 9 0 0 or 2 4 4 1 0 0 or 2 2 0 5 0 joules. Now we must use some algebra to find the velocity of the unsuspecting enemy whose mass is 6 3 k g (remember that the question specifies that all the energy goes into the enemy):
2 2 0 5 0 = 2 6 3 v 2 4 4 1 0 0 = 6 3 v 2 7 0 0 = v 2 7 0 0 = v
Therefore, the speed at which the enemy is bowled over is 7 0 0 s m . This is in s m already, so we've met the units requirement, and now we must round to the nearest hundredth to get:
2 6 . 4 6