you are part of a search and rescue mission that has been called out to look for

Question

you are part of a search and rescue mission that has been called out to look for a lost explorer. you've found the missing explorer , but you're separated from him by a 200m cliff and a 30 m wide river. To save his life you need to get a 5kg package of emergency supplies across the river. unfortunately you can't throw the package hard enough to make it across. you have a 1 kg rocket intended for launching flares. improvising you attach a sharpened stick to the rocket, which will impale the supplies. You then fire the rocket at ground level towards the supplies. what mininum speed must the rocket have just before the impact in order to save the explorer's life?

Explanation / Answer

The height of the cliff y = 200m
the horizontal distance x = 30m
y = 1/2 a t ^2
-200 = 0.5(-9.81)(t^2)
t = 6.38 sec, to fall 200 m
x = vt
30 = v (6.38)
v = 4.7 m/s to get across the

Therefore the package must be traveling 4.7 m/s horizontally at the top of the cliff to get across the raging river of death

From law of conservation momentum
( mR + mP)(4.7) = mR vR
therefore
vR = (1 + 5) (4.7) = 28.2 m/s

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