ðŸ‘‰ Try now NerdPal! Our new math app on iOS and Android

# Free Fall Calculator

## Get detailed solutions to your math problems with our Free Fall step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

Go!
Math mode
Text mode
Go!
1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

###  Difficult Problems

1

Solved example of free fall

A ball is dropped from the highest part of a building that has a height of 20 m. What time does it take to reach the ground?
2

What do we already know? We know the values for acceleration ($a$), initial velocity ($v_0$), distance ($y$), height ($y_0$) and want to calculate the value of time ($t$)

$a=-9.81\:m/s2,\:\: v_0=0,\:\: y=20\:m,\:\: y_0=0,\:\: t=\:?$
3

According to the initial data we have about the problem, the following formula would be the most useful to find the unknown ($t$) that we are looking for. We need to solve the equation below for $t$

$y=y_0+v_0t- \left(\frac{1}{2}\right)at^2$

4

We substitute the data of the problem in the formula and proceed to simplify the equation

$20=0+0t- \left(\frac{1}{2}\right)\cdot -9.81t^2$
5

Any expression multiplied by $0$ is equal to $0$

$20=0+0+4.905t^2$
6

Add the values $0$ and $0$

$20=4.905t^2$
7

Rearrange the equation

$4.905t^2=20$
8

Divide both sides of the equation by $4.905$

$\frac{4.905t^2}{4.905}=\frac{20}{4.905}$
9

Simplifying the quotients

$t^2=\frac{20}{4.905}$
10

Divide $20$ by $4.905$

$t^2=4.0775$

Removing the variable's exponent raising both sides of the equation to the power of $\frac{1}{2}$

$\left(t^2\right)^{\frac{1}{2}}=4.077472^{\frac{1}{2}}$

Divide $1$ by $2$

$\sqrt{t^2}=4.0775^{\frac{1}{2}}$

Simplify $\sqrt{t^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $0.5$

$t^{2\frac{1}{2}}$

Multiply $2$ times $0.5$

$t$

Multiply $2$ times $0.5$

$t=4.0775^{\frac{1}{2}}$

Divide $1$ by $2$

$t=\sqrt{4.0775}$

Calculate the power $\sqrt{4.0775}$

$t=2.0193$
11

Removing the variable's exponent raising both sides of the equation to the power of $\frac{1}{2}$

$t=2.0193$
12

The time of the ball is $2.0193$ s
The time of the ball is $2.0193$ s