By lowering a scoop as it skims the surface of a body of...

By lowering a scoop as it skims the surface of a body of water, the aircraft (nicknamed the "Super Scooper" is able to ingest $4.5 \mathrm{m}^{3}$ of fresh water during a 12 -second run. The plane then flies to a fire area and makes a massive water drop with the ability to repeat the procedure as many times as necessary. The plane approaches its run with a velocity of $280 \mathrm{km} / \mathrm{h}$ and an initial mass of $16.4 \mathrm{Mg}$. As the scoop enters the water, the pilot advances the throttle to provide an additional $300 \mathrm{hp}(223.8 \mathrm{kW})$ needed to prevent undue deceleration. Determine the initial deceleration when the scooping action starts. (Neglect the difference between the average and the initial rates of water intake.)

Key Concepts

Newton's Second Law

Newton’s Second Law underpins the analysis of the deceleration, stating that the net force acting on an object is equal to the rate of change of its momentum (or simply mass times acceleration for constant mass). In this problem, it is used to connect the extra force needed to accelerate the incoming water (and thus change the plane’s momentum) with the resulting deceleration of the aircraft.

Mass Flow Rate

The mass flow rate is the rate at which mass (in this case, water) is added to the aircraft as it scoops water. By determining the mass of water entering per unit time, one can compute the rate of change of momentum due to the water that must be accelerated from rest to the aircraft’s velocity. This concept is critical in analyzing the dynamics in variable-mass systems.

Power-Force-Velocity Relationship

The relationship between power, force, and velocity (where power is the product of force and velocity) is essential for quantifying the force provided by the additional engine power. In this context, the extra power requirement is used to counteract the decelerating force caused by the rapid intake of water, linking the energetic input directly to the force that influences the aircraft’s acceleration.

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