Question

4 kayla sets her physics book in the windowsill of an open window, 9.15 meters above the sidewalk. if she were to bump the book, so it began falling down towards the sidewalk, how long will it take until her book reaches the ground? 1.37 s 2.12 s 1.87 s 1.46 s

Explanation:

Step1: Identify the kinematic equation

The book is in free - fall, and the kinematic equation for vertical displacement is \(y = v_0t+\frac{1}{2}gt^{2}\). Since the book is bumped (initial vertical velocity \(v_0 = 0\)), the equation simplifies to \(y=\frac{1}{2}gt^{2}\), where \(y = 9.15\ m\) (the height of the book above the ground) and \(g = 9.8\ m/s^{2}\) (acceleration due to gravity).

Step2: Solve for \(t\)

From \(y=\frac{1}{2}gt^{2}\), we can solve for \(t\). Rearranging the formula gives \(t=\sqrt{\frac{2y}{g}}\).
Substitute \(y = 9.15\ m\) and \(g = 9.8\ m/s^{2}\) into the formula:
\(t=\sqrt{\frac{2\times9.15}{9.8}}=\sqrt{\frac{18.3}{9.8}}\approx\sqrt{1.867}\approx1.37\ s\)

Answer:

1.37 s