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Ch. 02 - Describing Motion: Kinematics in One Dimension
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
All textbooksGiancoli Douglas 5th editionCh. 02 - Describing Motion: Kinematics in One DimensionProblem 95a
Chapter 2, Problem 95a

Suppose a 65-kg person jumps from a height of 3.0 m down to the ground. What is the speed of the person just before landing (Chapter 2)?
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Identify the type of motion involved: This is a free-fall motion problem where the person is acted upon only by gravity. The initial velocity (v₀) is 0 m/s since the person starts from rest, and the acceleration is due to gravity (g = 9.8 m/s²).
Use the kinematic equation to relate the initial velocity, final velocity, acceleration, and displacement: \( v^2 = v_0^2 + 2g h \), where \( v \) is the final velocity, \( v_0 \) is the initial velocity, \( g \) is the acceleration due to gravity, and \( h \) is the height.
Substitute the known values into the equation: \( v_0 = 0 \), \( g = 9.8 \ \text{m/s}^2 \), and \( h = 3.0 \ \text{m} \). The equation simplifies to \( v^2 = 2(9.8)(3.0) \).
Solve for \( v \) by taking the square root of both sides: \( v = \sqrt{2(9.8)(3.0)} \).
Interpret the result: The value of \( v \) represents the speed of the person just before landing. Ensure the units are consistent and the result is in meters per second (m/s).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Gravitational Potential Energy

Gravitational potential energy (GPE) is the energy an object possesses due to its position in a gravitational field. It is calculated using the formula GPE = mgh, where m is mass, g is the acceleration due to gravity (approximately 9.81 m/s² on Earth), and h is the height above the ground. In this scenario, the person has potential energy at a height of 3.0 m, which will convert to kinetic energy as they fall.
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Kinetic Energy

Kinetic energy (KE) is the energy of an object in motion, given by the formula KE = 0.5mv², where m is mass and v is velocity. As the person falls, the gravitational potential energy is converted into kinetic energy, increasing their speed until they reach the ground. The speed just before landing can be determined by equating the initial potential energy to the kinetic energy at the moment of impact.
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Conservation of Energy

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. In this case, the gravitational potential energy of the person at the height of 3.0 m is transformed into kinetic energy as they fall. By applying this principle, we can calculate the speed of the person just before landing by setting the potential energy equal to the kinetic energy.
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