Verified Solution Science How Forces Affect Motion

What is the recoil velocity of a fire extinguisher of mass 10 kg, if it ejects 0.05 kg of CO₂ per second with a velocity of 20 m/s?

7 views 2 helpful Updated Jul 5, 2026
Solution ✔ Verified
  • A0.1 m/s
  • B0.05 m/s
  • C1 m/s
  • D0.2 m/s
Explanation

The force exerted by the CO₂ on the extinguisher is F = (Δm/Δt) * v_ejection = 0.05 kg/s * 20 m/s = 1 N. By Newton's Third Law, the reaction force on the extinguisher is also 1 N. Using F = M*a for the extinguisher, a = F/M = 1 N / 10 kg = 0.1 m/s². This is the initial acceleration; if asking for recoil velocity, it implies the velocity after a short duration, but the question is more about the immediate effect. If we consider momentum conservation over a very short Δt: Δp_extinguisher = -Δp_CO2. M_extinguisher * Δv_extinguisher = - Δm_CO2 * v_ejection. If this is rate, F = dP/dt. F_recoil = dP_CO2/dt = (dm/dt) * v_CO2 = 0.05 * 20 = 1 N. Recoil velocity isn't a direct result of this; it's a recoil *acceleration*. The question asks for "recoil velocity". This suggests finding the velocity imparted by the impulse over a short time, or a steady-state velocity if something else balances. Let's assume it asks for initial acceleration which can be interpreted as 'recoil effect'. Or it means, what instantaneous velocity does it gain if that's the only force. This is ambiguous.

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