The experimental race car is propelled by a rocket motor and...

The experimental race car is propelled by a rocket motor and is designed to reach a maximum speed $v=300 \mathrm{mi} / \mathrm{hr}$ under the thrust $T$ of its motor. Prior wind-tunnel tests disclose that the wind resistance at this speed is 225 lb. If the rocket motor is burning fuel at the rate of 3.5 lb/sec, determine the velocity $u$ of the exhaust gases relative to the car.

Key Concepts

Newton's Third Law of Motion

This law states that every action has an equal and opposite reaction. In the context of rocket propulsion, the gas expelled from the rocket engine produces an equal and opposite force on the vehicle, resulting in thrust. Understanding this principle is fundamental in analyzing how forces generated from expelled mass affect the motion of an object.

Rocket Thrust

Rocket thrust is the force generated by expelling mass (in the form of exhaust gases) at high velocity from the engine. It is calculated as the product of the mass flow rate and the exhaust velocity relative to the rocket. This concept is essential for determining how much force a rocket motor can produce to overcome opposing forces and achieve a desired speed.

Mass Flow Rate

Mass flow rate refers to the amount of mass expelled or consumed per unit time. In propulsion systems, it directly influences the magnitude of thrust when combined with the exhaust velocity. A proper understanding of the mass flow rate is necessary to relate the engine’s fuel consumption to the performance characteristics of the propulsion system.

Drag Force and Force Equilibrium

When a vehicle moves at a constant speed, such as the maximum speed in this scenario, the net external force acting on it is zero, meaning the thrust provided by the engine exactly balances the opposing forces like air resistance or drag. Recognizing the balance between thrust and drag is key to solving problems related to steady-state motion and understanding how various forces interact during motion.

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