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 3.8 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 1.2 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?

m/s

Explanation / Answer

The rocket will combine with packet and start from cliff with only horizontal velocity. and initial vertical component of velocity = 0m/s

Let the initial horizontal velocity ( combned packet) = V

Combined mass of rocket and packet = ( 1.2 + 3,8) = 5kg

Time taken by complete packet to cover a height of 200 m usng equation h = 0.5 gt^2

200 = 0.5(9.8)t^2

t= 6.39 sec apprx

Complete packet will take same time to cover a distance of 30 m horizontally

V = 30/ 6.39= 4.69 m/s apprx ( horizontal velocity)

Horizontal velocty will not undero any change as there is no acceleration,

Using the conservation of momnetum

1.2( U) = 5( 4.69)

U( velocity of rocket before impact) = 19. 54 m/s apprx

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