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Ch 03: Motion in Two or Three Dimensions
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 14th EditionCh 03: Motion in Two or Three DimensionsProblema 12d
Capitolo 3, Problema 12d

A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. How far has the football traveled horizontally during this time?

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1
Identify the horizontal motion of the football as uniform motion since there is no air resistance affecting it. The horizontal velocity remains constant at 20.0 m/s.
Determine the time of flight for the football. Since the vertical motion is independent of the horizontal motion, use the vertical component to find the time. The vertical motion is subject to gravity, so use the kinematic equation: vf = vi + at, where vf is the final vertical velocity (0 m/s at the peak), vi is the initial vertical velocity (12.0 m/s), and a is the acceleration due to gravity (-9.8 m/s²).
Solve for the time to reach the peak using the equation: t = (vf - vi)/a. Since the time to reach the peak is half of the total time of flight, multiply the result by 2 to find the total time the football is in the air.
Calculate the horizontal distance traveled using the formula for distance in uniform motion: d = vht, where vh is the horizontal velocity (20.0 m/s) and t is the total time of flight calculated in the previous step.
Substitute the values into the distance formula to find the horizontal distance traveled by the football during its flight.

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Projectile Motion

Projectile motion involves the motion of an object thrown into the air, subject to only the acceleration of gravity. It can be analyzed by separating the motion into horizontal and vertical components. The horizontal motion is uniform, while the vertical motion is uniformly accelerated due to gravity.
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Introduction to Projectile Motion

Horizontal Velocity

Horizontal velocity refers to the constant speed at which an object moves along the horizontal axis. In projectile motion, this component remains unchanged throughout the flight, as there is no horizontal acceleration when air resistance is ignored. It is crucial for calculating the horizontal distance traveled.
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Solving Horizontal Launch Problems

Time of Flight

Time of flight is the total time an object remains in the air during projectile motion. It is determined by the vertical motion, specifically the time taken for the object to reach its peak and return to the ground. This duration is essential for calculating how far the object travels horizontally.
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Velocity-Time Graphs & Acceleration
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A rookie quarterback throws a football with an initial upward velocity component of 12.0 m/s and a horizontal velocity component of 20.0 m/s. Ignore air resistance. How much time (after it is thrown) is required for the football to return to its original level? How does this compare with the time calculated in part (a)?

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