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Chapter 2: Problem 78

You're staring idly out your dorm window when you see a water balloon fall past. If the balloon takes 0.22 s to cross the 1.3-m-high window, from what height above the window was it dropped?

Short Answer

Expert verified
The height above the window from which the water balloon was dropped is calculated by adding the height of the balloon's fall to the height of the window.

Step by step solution

01

Identify Known Variables

In this problem, two variables are known: the time the balloon takes to cross the window (t = 0.22s), and the height of the window (d = 1.3m). The acceleration due to gravity (a = 9.8 m/s²) is also known, as it is a constant.
02

Application Of The Equation Of Motion

The equation used to calculate the initial velocity (u), given the displacement (d), time (t) and gravity (a) is: \(d = ut + 0.5at^2\). As we want to find \(u\), we can rearrange this equation to give: \(u = (d - 0.5at^2) / t\). Substitute the known values into this equation to calculate \(u\).
03

Finding The Height From Which The Balloon Was Dropped

To find the height from which the balloon was dropped, you need to calculate the distance the balloon had fallen before it passed the window. This can be done by using the equation of motion \(d = ut + 0.5at^2\), where \(d\) is the distance (height), \(u\) is the initial speed, \(t\) is time, and \(a\) is acceleration due to gravity. And since the balloon was dropped, the initial speed \(u = 0\). Therefore, the equation simplifies to \(d = 0.5at^2\). Insert the calculated initial velocity and known time into this equation to obtain the height.
04

Sum The Height Of The Balloon's Fall To The Height Of The Window

Finally, you need to add the height of the window to the calculated height of the balloon’s fall before reaching the window to get the total height from which the balloon was dropped.

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