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Ch 02: Motion Along a Straight Line
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 02: Motion Along a Straight LineProblema 37
Capitolo 2, Problema 37

A juggler throws a bowling pin straight up with an initial speed of 8.208.20 m/s. How much time elapses until the bowling pin returns to the juggler's hand?

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Identify the key variables: initial velocity \( v_0 = 8.20 \) m/s, acceleration due to gravity \( g = 9.81 \) m/s² (acting downward), and final velocity \( v = 0 \) m/s at the peak of the throw.
Use the kinematic equation \( v = v_0 - gt \) to find the time \( t \) it takes for the bowling pin to reach its highest point. Set \( v = 0 \) and solve for \( t \).
Calculate the time to reach the peak using \( t = \frac{v_0}{g} \). This gives the time for the pin to stop rising.
Since the time to ascend is equal to the time to descend, multiply the time calculated in the previous step by 2 to find the total time for the pin to return to the juggler's hand.
Summarize the process: The total time elapsed is twice the time taken to reach the peak, which accounts for both the upward and downward journey of the bowling pin.

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Kinematics Equations

Kinematics equations describe the motion of objects without considering the forces that cause the motion. For an object thrown vertically, the key equation is: final velocity = initial velocity + (acceleration × time). In this scenario, the acceleration is due to gravity, which is approximately -9.81 m/s², acting downward.
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Kinematics Equations

Free Fall Motion

Free fall motion refers to the movement of an object under the influence of gravitational force only. When the juggler throws the bowling pin upwards, it decelerates until it reaches its peak height, where the velocity is zero, and then accelerates back down. The time to reach the peak is equal to the time to return to the original position.
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Vertical Motion & Free Fall

Symmetry of Projectile Motion

In projectile motion, especially vertical throws, the time taken to ascend to the highest point is equal to the time taken to descend back to the starting point. This symmetry helps in calculating the total time of flight by simply doubling the time taken to reach the peak height, which can be found using the initial velocity and gravitational acceleration.
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Projectile Motion with Energy
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