Question

name: jairomoirrez
free fall classwork 2023
period: 7
instructions: show work for each problem below. see me to get stamps. please only 1 stamp at a time. you must get at least 1 stamp in class today. if you do not finish, take the assignment for homework and bring it back at the start of next class.

1. a four - story building has a height of 13 meters. a ball is dropped from the top of the building from rest. how long does it take for the ball to fall to the ground?

a. solve for the time \t\ in terms of the variables in the equation. dont plug any numbers in yet, other than 0. show all work below.
b. plug in numbers for the above problem and solve. remember to include units.

Explanation:

Step1: Identify the free - fall formula

The kinematic equation for free - fall is $d = v_0t+\frac{1}{2}gt^2$. Since the ball is dropped from rest, $v_0 = 0$. So the equation simplifies to $d=\frac{1}{2}gt^2$.

Step2: Solve for t in terms of variables

Starting with $d=\frac{1}{2}gt^2$, we first multiply both sides by 2 to get $2d = gt^2$. Then divide both sides by $g$: $t^2=\frac{2d}{g}$. Taking the square - root of both sides, we have $t=\sqrt{\frac{2d}{g}}$.

Step3: Plug in values

We know that $d = 13$ meters and $g = 9.8\ m/s^2$. Substituting these values into the formula $t=\sqrt{\frac{2d}{g}}$, we get $t=\sqrt{\frac{2\times13}{9.8}}=\sqrt{\frac{26}{9.8}}\approx\sqrt{2.653}\approx1.63\ s$.

Answer:

a. $t=\sqrt{\frac{2d}{g}}$
b. $t\approx1.63\ s$