(a) At what speed would a 2.00 ×10^4-kg airplane have to fly to have a momentum of 1.60 ×10^9 kg

step 1 Speed is given by momentum over mass. The momentum is given by 1 .6 times 10 to the 9 kilogram m

(a) At what speed would a 2.00 ×10^4-kg airplane have to fly...

(a) At what speed would a $2.00 \times 10^{4}-\mathrm{kg}$ airplane have to fly to have a momentum of $1.60 \times 10^{9} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ (the same as the ship's momentum in the problem above)? (b) What is the plane's momentum when it is taking off at a speed of $60.0 \mathrm{m} / \mathrm{s} ?(\mathrm{c})$ if the ship is an aircraft carrier that launches these airplanes with a catapult, discuss the implications of your answer to (b) as it relates to recoil effects of the catapult on the ship.

Key Concepts

Conservation of Momentum

The conservation of momentum principle holds that in a closed system with no external forces, the total momentum remains constant before and after an event, such as a collision or a launch. This concept is vital when analyzing interactions like the recoil experienced by a catapult launching an airplane, ensuring that the momentum gained by the airplane is balanced by an equal and opposite momentum imparted to the aircraft carrier.

Impulse

Impulse is defined as the product of the force applied to an object and the time duration over which it is applied, and it corresponds to the change in momentum of that object. This concept is important in understanding how a short, forceful push—like that from a catapult—can result in a significant momentum change, thereby linking the applied forces to measured outcomes in dynamics.

Momentum

Momentum is a fundamental concept in physics defined as the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction, and is crucial in understanding how objects move and interact. The equation p = m × v illustrates that momentum increases with either mass or speed, making it central to solving motion and collision problems.

Newton's Third Law

Newton's Third Law states that for every action there is an equal and opposite reaction. This principle explains that when one object exerts a force on another, the second object exerts a force of equal magnitude but in the opposite direction on the first. This is particularly relevant in scenarios like the airplane being launched from a carrier, where the force of the catapult not only propels the airplane forward but also causes a recoil effect on the carrier.

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