Question

a student drops a marble from a tower. neglect drag. how long did it take for the marble to reach the ground? how tall is the tower?

Explanation:

Step1: Identify the relevant formula

The motion of the marble is free - fall motion. The time - of - fall $t$ and the height $h$ of the tower can be found using the equations of motion. The time of fall is given directly as $t = 4.3\ s$ (from the image). The formula for the height of an object in free - fall starting from rest ($v_0=0$) is $h = v_0t+\frac{1}{2}gt^2$. Since $v_0 = 0$, the formula simplifies to $h=\frac{1}{2}gt^2$, where $g = 9.8\ m/s^2$.

Step2: Calculate the height of the tower

Substitute $t = 4.3\ s$ and $g = 9.8\ m/s^2$ into the formula $h=\frac{1}{2}gt^2$.
$h=\frac{1}{2}\times9.8\times(4.3)^2$
$h = 4.9\times18.49$
$h=90.601\ m$

Answer:

How long did it take for the marble to reach the ground? 4.3 s
How tall is the tower? 90.601 m