Question

an object is dropped from a platform 100 feet high. ignoring wind resistance, how long will it take to reach the ground? ____ s
○ 4.5
○ 3.2
○ 1.8
○ 2.5

Explanation:

Step1: Recall the free - fall formula

The formula for the distance \(d\) an object falls in free - fall (ignoring air resistance) is \(d = \frac{1}{2}gt^{2}\), where \(d\) is the distance fallen, \(g\) is the acceleration due to gravity, and \(t\) is the time. In the English system, the acceleration due to gravity \(g=32\space ft/s^{2}\), and the initial velocity \(v_0 = 0\) (since the object is dropped)

The distance \(d = 100\space ft\), and the formula becomes \(d=\frac{1}{2}gt^{2}\), so we can solve for \(t\):

First, rewrite the formula to solve for \(t\):

From \(d=\frac{1}{2}gt^{2}\), we get \(t^{2}=\frac{2d}{g}\), then \(t=\sqrt{\frac{2d}{g}}\)

Step2: Substitute the values of \(d\) and \(g\)

We know that \(d = 100\space ft\) and \(g = 32\space ft/s^{2}\)

Substitute these values into the formula for \(t\):

\(t=\sqrt{\frac{2\times100}{32}}=\sqrt{\frac{200}{32}}=\sqrt{6.25} = 2.5\space s\)

Answer:

2.5