Question

a student drops a ball off the top of building and records that the ball takes 3.07s to reach the ground. determine all unknowns and answer the following questions. neglect drag. what was the balls speed just before striking the ground? from what height was the ball dropped?

Explanation:

Step1: Identify the relevant kinematic - equation for speed

We use the equation $v = v_0+at$. The initial velocity $v_0 = 0$ (dropped ball), $a = g= 9.8\ m/s^{2}$ and $t = 3.07\ s$.
$v=0 + gt$

Step2: Calculate the speed

Substitute $g = 9.8\ m/s^{2}$ and $t = 3.07\ s$ into the equation.
$v=9.8\times3.07$
$v = 30.086\ m/s$

Step3: Identify the relevant kinematic - equation for height

We use the equation $y=v_0t+\frac{1}{2}at^{2}$. Since $v_0 = 0$, the equation simplifies to $y=\frac{1}{2}gt^{2}$.

Step4: Calculate the height

Substitute $g = 9.8\ m/s^{2}$ and $t = 3.07\ s$ into the equation.
$y=\frac{1}{2}\times9.8\times(3.07)^{2}$
$y = 4.9\times9.4249$
$y=46.18201\ m$

Answer:

What was the ball's speed just before striking the ground? 30.086 m/s
From what height was the ball dropped? 46.18201 m