I am a little stumped on this problem, my prof advised me toset two systems equa

Question

I am a little stumped on this problem, my prof advised me toset two systems equal to each other and I am just not seeing itthrough to completion.
A hot-air balloon has just lifted off and is rising at the constantrate of 2.3 m/s. Suddenlyone of the passengers realizes she has left her camera on theground. A friend picks it up and tosses it straight upward. If thepassenger is 3.8 m above herfriend when the camera is tossed, what is the minimum initial speedof the camera if it is to just reach the passenger? (Hint: When thecamera is thrown with its minimum speed, its speed on reaching thepassenger is the same as the speed of the passenger. I am a little stumped on this problem, my prof advised me toset two systems equal to each other and I am just not seeing itthrough to completion.

Explanation / Answer

the speed of balloon = u = 2.3 Initial height of balloon at time t=0 is h = 3.8 let the launch speed of camera be v. Let the flight time be t. then, distance traveled by camera = h + ut = (v+u)t/2 h = (v-u)t/2 but u = v - gt t = (v-u)/g so h = (v-u)^2 /(2g) (v-u)^2 = 2gh v = u + (2hg) = 2.3 + (2*9.8*3.8) = 10.9 m/s

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