CATapult!

A 9 k g 9 \mathrm{kg} cat (including armor, so he isn't hurt by this) is launched at 70 m s 70 \mathrm{\frac{m}{s}} at an unsuspecting enemy. The enemy has a mass of 63 k g 63 \mathrm{kg} . Assuming a conservation of energy, with the cat retaining no energy, at what speed is the enemy bowled over? (Use units of m s \mathrm{\frac{m}{s}} and round to the nearest hundredth.)


The answer is 26.46.

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1 solution

Wwt Manahan
May 13, 2015

Remember that the energy of a moving object, with some mass m m and some velocity v v , is m v 2 2 \frac{mv^2}{2} . Therefore, the energy of the cat is 9 7 0 2 2 \frac{9\cdot70^2}{2} or 9 4900 2 \frac{9\cdot4900}{2} or 44100 2 \frac{44100}{2} or 22050 22050 joules. Now we must use some algebra to find the velocity of the unsuspecting enemy whose mass is 63 k g 63\mathrm{kg} (remember that the question specifies that all the energy goes into the enemy):

22050 = 63 v 2 2 22050 = \frac{63v^2}{2} 44100 = 63 v 2 44100 = 63v^2 700 = v 2 700 = v^2 700 = v \sqrt{700} = v

Therefore, the speed at which the enemy is bowled over is 700 m s \sqrt{700}\mathrm{\frac{m}{s}} . This is in m s \mathrm{\frac{m}{s}} already, so we've met the units requirement, and now we must round to the nearest hundredth to get:

26.46 26.46

How comes the result doesn't come out the same from impulses conservation? m c a t v c a t = M e n e m y v e n e m y m_{cat} \cdot v_{cat} = M_{enemy} \cdot v_{enemy}

Zyberg NEE - 3 years, 3 months ago

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