You have just landed on Planet X. You take out a 100 -g...

You have just landed on Planet X. You take out a 100 -g ball, release it from rest from a height of $10.0 \mathrm{m},$ and measure that it takes 2.2 $\mathrm{s}$ to reach the ground. You can ignore any force on the ball from the atmosphere of the planet. How much does the $100-\mathrm{g}$ ball weigh on the surface of Planet $\mathrm{X} ?$

Key Concepts

Neglecting Air Resistance

Neglecting air resistance simplifies the analysis of free fall by assuming that the only force acting on the falling object is gravity. This assumption allows the use of simple kinematic equations to accurately predict the motion of the object in vacuum conditions or environments where air resistance is minimal.

Gravitational Acceleration

Gravitational acceleration is the rate at which an object accelerates when falling under the influence of gravity alone. It is a fundamental concept in physics used to describe how the velocity of an object changes with time during free fall, and it is typically determined by the local mass distribution that creates the gravitational field.

Free-Fall Kinematics

The kinematics of free fall involve equations that relate displacement, time, and acceleration under the influence of gravity, assuming that air resistance is negligible. This is commonly used in problems where an object is dropped from a known height and the time to hit the ground is measured, allowing one to calculate the acceleration due to gravity using the equation s = ½gt².

Weight Calculation

Weight is the force exerted on an object due to gravity, calculated by multiplying the mass of the object by the local gravitational acceleration (W = mg). This concept is crucial in understanding that while mass is constant, weight can vary from one planetary body to another due to differences in gravitational pull.

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