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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: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 02 - Describing Motion: Kinematics in One DimensionProblema 100
Capitolo 2, Problema 100

Bill can throw a ball vertically at a speed 1.5 times faster than Joe can. How many times higher will Bill's ball go than Joe's?

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Identify the relationship between the maximum height of a projectile and its initial velocity. The maximum height (h) is given by the formula: h=v22g, where v is the initial velocity and g is the acceleration due to gravity.
Recognize that Bill's initial velocity is 1.5 times Joe's initial velocity. Let Joe's initial velocity be vj, so Bill's initial velocity is 1.5vj.
Substitute the initial velocities into the height formula for both Bill and Joe. For Joe: hj=vj22g. For Bill: hb=1.5vj22g.
Simplify the expression for Bill's height. Using 1.52=2.25, Bill's height becomes: hb=2.25vj22g.
Find the ratio of Bill's height to Joe's height: hbhj=2.251. This shows that Bill's ball will go 2.25 times higher than Joe's.

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Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this context, understanding kinematics is essential to analyze how the initial speed of the ball affects its maximum height.
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Projectile Motion

Projectile motion refers to the motion of an object that is thrown or projected into the air, subject only to the acceleration of gravity. For vertical throws, the maximum height reached by the projectile can be calculated using the initial velocity and the acceleration due to gravity. This concept is crucial for determining how the height of Bill's throw compares to Joe's.
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Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In the context of projectile motion, the kinetic energy of the ball at the moment of release is converted into gravitational potential energy at its peak height. This relationship helps in calculating the heights reached by Bill and Joe based on their respective throwing speeds.
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Conservation Of Mechanical Energy
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