A small rocket with mass 20.0 kg is moving in free fall toward the earth. Air resistance can be

step 1 High. In the given problem, mass of the rocket is given as m is equal to 20 kilogram. Its height

A small rocket with mass 20.0 kg is moving in free fall...

A small rocket with mass $20.0 \mathrm{~kg}$ is moving in free fall toward the earth. Air resistance can be neglected. When the rocket is $80.0 \mathrm{~m}$ above the surface of the earth, it is moving downward with a speed of $30.0 \mathrm{~m} / \mathrm{s}$. At that instant the rocket engines start to fire and produce a constant upward force $F$ on the rocket. Assume the change in the rocket's mass is negligible. What is the value of $F$ if the rocket's speed becomes zero just as it reaches the surface of the earth, for a soft landing? (Hint: The net force on the rocket is the combination of the upward force $F$ from the engines and the downward weight of the rocket.)

Key Concepts

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. This principle is essential when analyzing problems where multiple forces are acting on an object, as it allows us to determine the resulting acceleration from the combination of forces such as gravity and any applied forces.

Kinematic Equations for Constant Acceleration

Kinematic equations relate an object's initial velocity, final velocity, acceleration, and displacement when the acceleration is constant. These equations are used to calculate how changes in speed over a known distance are connected to the acceleration, which in turn can be used to infer the net force acting on the object.

Gravitational Force

Gravitational force is the attractive force exerted by the Earth on objects, calculated as the product of the object's mass and the acceleration due to gravity. It plays a fundamental role in motion problems by contributing a constant downward force that must be overcome or countered by other forces.

Work-Energy Theorem

The work-energy theorem equates the work done on an object by the net force to the change in its kinetic energy. This concept is useful in analyzing situations where forces act over a distance to change an object's speed, providing a way to link the energy considerations with force calculations.

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