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Calculating Ball Displacement Off a Table: A Physics & Calculus Insigh
Chapter 3, Problem 62(choose chapter or problem)
After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by
\(\overrightarrow{v}=1.2\,\widehat{i}-9.8t\ \widehat{j}\)
where \(\overrightarrow{v}\) is in meters per second and t is in seconds. The ball’s displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by
\(\Delta \overrightarrow{r}=\int\limits_{0}^{0.380}{\overrightarrow{v}dt}\)
To perform the integral, you can use the calculus theorem
\(\int{\left[ A+Bf\left( x \right) \right]dx}=\int{Adx}+B\int{f\left( x \right)dx} \)
You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.
Questions & Answers
QUESTION:
After a ball rolls off the edge of a horizontal table at time t = 0, its velocity as a function of time is given by
\(\overrightarrow{v}=1.2\,\widehat{i}-9.8t\ \widehat{j}\)
where \(\overrightarrow{v}\) is in meters per second and t is in seconds. The ball’s displacement away from the edge of the table, during the time interval of 0.380 s for which the ball is in flight, is given by
\(\Delta \overrightarrow{r}=\int\limits_{0}^{0.380}{\overrightarrow{v}dt}\)
To perform the integral, you can use the calculus theorem
\(\int{\left[ A+Bf\left( x \right) \right]dx}=\int{Adx}+B\int{f\left( x \right)dx} \)
You can think of the units and unit vectors as constants, represented by A and B. Perform the integration to calculate the displacement of the ball from the edge of the table at 0.380 s.
ANSWER:Step 1 of 2
Consider the given data as follows.
The speed of the ball is \(\overrightarrow{v}=1.2\,\widehat{i}-9.8t\ \widehat{j}\).
The time is 0.380 s.
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Calculating Ball Displacement Off a Table: A Physics & Calculus Insigh
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Learn how to compute the displacement of a ball rolling off a table using calculus. Through the integration of velocity over a specific time interval, determine the ball's position. Uncover the mathematics behind real-world motion scenarios.