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 200-m-high cliff and a 30-m-wide raging river. To save his life, you need to get a 5.4 kg package of emergency supplies across the river. Unfortunately, you can't throw the package hard enough to make it across. Fortunately, you happen to have a 1.6 kg rocket intended for launching flares. Improvising quickly, you attach a sharpened stick to the front of the rocket, so that is will impale itself into the package of supplies, then fire the rocket at ground level toward the supplies. What minimum speed must the rocket have just before impact in order to save the explorer's life?

Explanation / Answer

Time taken to Fall 200m
S = u*t - 1/2*a*t^2
200 = 0 - 1/2 *9.8*t^2
t = 6.38 sec

Horizontal Distance travelled , d = 30 m
d = vt
30 = v (6.38)
v = 4.7 m/s to get across the river

Using Momentum Conservation -
mass of rocket * velocity + mass of box * velocity = mass of box and rocket * velocity
1.6 kg * v + 5kg * 0 = (1.6 + 5.4)kg * 4.7m/s
1.6 * v = 7*4.6
v = 20.56 m/s
Minimum speed must the rocket have , v = 20.56 m/s

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