Question

question 10
a penny is dropped from a 170 meter building. with no air resistance, how long will it take for the penny to hit the ground?
10 pts

Explanation:

Step1: Use the free - fall formula

The formula for the height \(h\) of an object in free - fall is \(h = v_0t+\frac{1}{2}gt^2\). Since the penny is dropped (\(v_0 = 0\) m/s) and \(g = 9.8\) m/s², the formula simplifies to \(h=\frac{1}{2}gt^2\). We know \(h = 170\) m.

Step2: Solve for \(t\)

Substitute \(h = 170\) m and \(g = 9.8\) m/s² into \(h=\frac{1}{2}gt^2\). We get \(170=\frac{1}{2}\times9.8t^2\). First, simplify the equation: \(170 = 4.9t^2\). Then, \(t^2=\frac{170}{4.9}\approx34.69\). Take the square root of both sides: \(t=\sqrt{34.69}\approx5.9\) s.

Answer:

\(t\approx5.9\) s