A student with mass 45 kg jumps off a high diving board. Using 6.0 ×10^24 kg for the mass of the

step 1 Question number 25, when a person jumps from a height, then his motion is accelerated by the acc

A student with mass 45 kg jumps off a high diving board....

A student with mass 45 $\mathrm{kg}$ jumps off a high diving board. Using $6.0 \times 10^{24} \mathrm{kg}$ for the mass of the earth, what is the acceleration of the earth toward her as she accelerates toward the earth with an acceleration of 9.8 $\mathrm{m} / \mathrm{s}^{2}$ ? Assume that the net force on the earth is the force of gravity she exerts on it.

Key Concepts

Mass Ratio and Inverse Proportionality

The concept of mass ratio and inverse proportionality is critical in understanding the differing accelerations resulting from the same gravitational force. Since the Earth's mass is many orders of magnitude larger than the student's mass, the Earth's acceleration due to the gravitational pull of the student is correspondingly much smaller.

Gravitational Force

Gravitational force is the attractive force between two masses, as described by Newton's Law of Universal Gravitation. In this context, it explains the mutual attraction between the student and the Earth and is the force that causes both objects to accelerate towards each other.

Newton's Third Law of Motion

Newton's Third Law states that for every action, there is an equal and opposite reaction. This means that when the student exerts a gravitational force on the Earth, the Earth exerts an equal force on the student, which is the conceptual basis for the interaction between them despite the Earth's vastly different mass.

Newton's Second Law of Motion

Newton's Second Law relates force, mass, and acceleration through the equation F = ma. This law is used to understand how the same force causes different accelerations when applied to objects with different masses, explaining why the Earth's acceleration is extremely small compared to that of the student.

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