Suppose that a person takes 0.5 s to react and move his hand...

Suppose that a person takes 0.5 s to react and move his hand to catch an object he has dropped. (a) How far does the object fall on Earth, where $g=9.8 \mathrm{m} / \mathrm{s}^{2} ?$ (b) How far does the object fall on the Moon, where the acceleration due to gravity is $1 / 6$ of that on Earth?

Key Concepts

Uniformly Accelerated Motion

This concept refers to motion where the acceleration remains constant throughout, enabling the use of kinematic equations to predict displacement and velocity over time. In problems involving free fall, the displacement is calculated using the formula distance = ½ × acceleration × time² when the object starts from rest.

Gravitational Acceleration

Gravitational acceleration is the rate at which an object accelerates due to the force of gravity. On Earth, this acceleration is approximately 9.8 m/s², while on other celestial bodies like the Moon, it differs based on the body's mass and radius. The lesser gravitational acceleration on the Moon results in objects falling more slowly compared to Earth.

Free Fall Motion

Free fall motion describes the movement of an object solely under the influence of gravity, in the absence of other forces like air resistance. This simplifies the analysis by allowing the direct application of kinematic equations to determine factors such as displacement over a given time interval.

Reaction Time in Kinematics

In physics problems, reaction time refers to the delay between a stimulus and the corresponding response. When calculating how far an object falls before being caught, the reaction time represents the duration during which the object is in free fall, forming the time element in the kinematic calculation.

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