Question

question 9
if the penny is thrown horizontally at 25 m/s from the 170 meter building, how long will it take for the penny to hit the ground?

Explanation:

Step1: Analyze the vertical motion

The vertical displacement \(y = 170\) m (height of the building), the initial vertical velocity \(u_y=0\) m/s (thrown horizontally), and the acceleration due to gravity \(g = 9.8\) m/s². Use the equation \(y=u_y t+\frac{1}{2}gt^{2}\). Substituting \(u_y = 0\), we get \(y=\frac{1}{2}gt^{2}\).

Step2: Solve for time \(t\)

From \(y=\frac{1}{2}gt^{2}\), we can solve for \(t\). Rearranging the formula gives \(t=\sqrt{\frac{2y}{g}}\). Plugging in \(y = 170\) m and \(g=9.8\) m/s²: \(t=\sqrt{\frac{2\times170}{9.8}}\).

$$t=\sqrt{\frac{340}{9.8}}\approx\sqrt{34.69}\approx 5.9$$

s

Answer:

The time it takes for the penny to hit the ground is approximately \(5.9\) s.