A ten year old boy (26 kg) sits on a wheeled office chair (16kg) holding a fire extinguisher (18kg when empty). He points the discharge horn to the right and ejects 9kg of carbon dioxide at 20m/s. What is his velocity after the fire extinguisher is emptied

30m/s

Explanation:

Suppose there's no friction between the office chair and the floor. The only thing that impact the motion of the boy is the ejected carbon dioxide. We can apply the law of momentum conservation to find the his (the boy, the chair and the empty extinguisher) after the extinguisher is emptied.

Before the ejects, the system momentum is 0, due to at rest and no speed

After the ejects, momentum of the carbon dioxide is

9*20 = 180 kg m/s

The momentum of his is then

P + 180 = 0

P = -180

MV = -180

(26 + 16 + 18)V = - 180

V = -180/(26 + 16 + 18) = -30 m/s

So he would have a speed of 30m/s in the opposite of the ejected carbon dioxide direction

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