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An object is dropped from rest out of the window of a building, and the time to hit the ground is found to be 5 seconds. The same object is then dropped from rest out of a window twice as high above the ground as the original window. The time it takes the object to hit the ground is closest to:

An object is dropped from rest out of the window of a building and the time to hit the ground is found to be 5 seconds The same object is then dropped from rest class=

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ANSWER:

7 s

STEP-BY-STEP EXPLANATION:

Given:

u = 0m/s

t = 5 sec

g = 9.8 m/s^2

The first thing is to calculate the height of the building, using the following formula:

[tex]\begin{gathered} s=ut+\frac{1}{2}gt^2 \\ \text{ Replacing} \\ s=0\cdot5+\frac{1}{2}\cdot9.8\cdot5^2 \\ s=122.5\text{ m} \end{gathered}[/tex]

Now, we apply the same formula, but we substitute the double value of the distance and solve for t, just like this:

[tex]\begin{gathered} 2\cdot122.5=\frac{1}{2}\cdot9.8\cdot\: t^2 \\ 9.8\cdot t^2=245\cdot2 \\ t^2=\frac{490}{9.8} \\ t=\sqrt[]{50} \\ t=7.07\text{ sec} \\ t\approx7\text{ sec} \end{gathered}[/tex]

The time it takes for the object to fall is 7 seconds.

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