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?

Ch 02: Motion Along a Straight Line

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

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Young & Freedman Calc 15th Edition

Ch 02: Motion Along a Straight Line

Problem 33

Chapter 2, Problem 33

A juggler throws a bowling pin straight up with an initial speed of $8.20$ m/s. How much time elapses until the bowling pin returns to the juggler's hand?

Verified step by step guidance

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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Key Concepts

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

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.

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.

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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Textbook Question

You throw a glob of putty straight up toward the ceiling, which is $3.60$ m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is $9.50$ m/s. What is the speed of the putty just before it strikes the ceiling?

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Textbook Question

You throw a glob of putty straight up toward the ceiling, which is $3.60$ m above the point where the putty leaves your hand. The initial speed of the putty as it leaves your hand is $9.50$ m/s. How much time from when it leaves your hand does it take the putty to reach the ceiling?

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A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$ -m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. What is the speed of the rock just before it hits the street?

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Textbook Question

A small rock is thrown vertically upward with a speed of $22.0$ m/s from the edge of the roof of a $30.0$ -m-tall building. The rock doesn't hit the building on its way back down and lands on the street below. Ignore air resistance. How much time elapses from when the rock is thrown until it hits the street?

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