Question

1. analysis

a. reaction time
to begin with, we must relate a dropped distance to a time to fall that distance. using your knowledge of kinematics and free - fall motion, determine the time to fall a distance y. find this symbolically. show your work below. you should arrive at t = (\frac{2y}{g})^{1/2}

Explanation:

Step1: Recall kinematic equation

The kinematic equation for free - fall motion is $y = v_0t+\frac{1}{2}gt^2$. Since the initial vertical velocity $v_0 = 0$ (dropped object), the equation simplifies to $y=\frac{1}{2}gt^2$.

Step2: Solve for time $t$

Starting from $y=\frac{1}{2}gt^2$, we first multiply both sides by 2 to get $2y = gt^2$. Then divide both sides by $g$: $\frac{2y}{g}=t^2$. Finally, take the square - root of both sides. Considering the physical context (time cannot be negative for this motion), we have $t = (\frac{2y}{g})^{\frac{1}{2}}$.

Answer:

$t = (\frac{2y}{g})^{\frac{1}{2}}$