You have an internship with the Exploratorium, in San Francisco, and your superv

Question

You have an internship with the Exploratorium, in San Francisco, and your supervisor (a chemist) has a great new idea for a demo. Two small balloons will be filled with different chemicals that create a big burst of light when they react. One will be dropped from the ceiling and another will be shot up from the floor, released at the same moment. The reaction will happen best if the balloon heading upwards is traveling at the same speed as the balloon heading downwards, when they collide. One engineer is building the rig to drop the balloon, but doesn’t know the exact height it will be dropped from yet. Another is building the balloon launcher, which will have an adjustable launch speed. Your supervisor is worried about the height that the collision will occur at, and wants to make sure it is above everyone’s head. What can you say?

Explanation / Answer

Solution:

Balloon-A: The one dropped from the ceiling

Balloon-B: The one that is shot up from the floor

Here;

as we want the balloon heading upwards is traveling at the same speed as the balloon heading downwards

=> height of balloon-A will depend on the velocity by which you need to shot balloon-B

let's say the initial height of baloon-A is 'H' and 'h' wrt. the instance where they collide.

=> we need to match the speed at an instance

=> v1 = -v2 (negative for opposite direction)

=> h = H/2

Hence; the initial speed of Balloon-B should be sqrt(gH) with Ballon-A initial height be H.

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