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 Example

 Solved Problems

 Difficult Problems

Here, we show you a step-by-step solved example of free fall. This solution was automatically generated by our smart calculator:

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?

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 ($t$)

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

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 $t$

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

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

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

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

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

Add the values $0$ and $0$

$20=4.905t^2$

Rearrange the equation

$4.905t^2=20$

Divide both sides of the equation by $4.905$

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

Simplifying the quotients

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

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 $\sqrt{4.0775}$

$t=2.0193$

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

$t=2.0193$

The complete answer is

The time of the ball is $2.0193$ s

 Final Answer