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 a200-m-high cliff and a 30-m-wide raging river. To save his life, you need to get a 5.0 kg package of emergency supplies across the river. Unfortunately, you can'tthrow the package hard enough to make it across. Fortunately, you happen to have a 1.0 kg rocket intended for launching flares. Improvising quickly, you attach asharpened stick of negligible mass to the front of the rocket, so that it will impale itself into the package of supplies, then fire the rocket at ground level towardthe supplies.

Part A: What minimum speed must the rocket have just before impact in order to save the explorer's life?

Answer 1

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