Free Fall Rechner

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Symbolischer Modus

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 Schwierige Probleme

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- -9.81\cdot \left(\frac{1}{2}\right)t^2

Multiply the fraction and term in $9.81\cdot \left(\frac{1}{2}\right)t^2$

20=0+0t+\frac{9.81\cdot 1}{2}t^2

Multiply $9.81$ times $1$

20=0+0t+\frac{9.81}{2}t^2

Multiply the fraction and term in $9.81\cdot \left(\frac{1}{2}\right)t^2$

20=0+0t+\frac{9.81}{2}t^2

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

20=0+\frac{9.81}{2}t^2

$x+0=x$ , where $x$ is any expression

20=\frac{9.81}{2}t^2

Rearrange the equation

\frac{9.81}{2}t^2=20

Multiply both sides of the equation by $2$

9.81t^2=20\cdot 2

Multiply $20$ times $2$

9.81t^2=40

Multiply both sides of the equation by $2$

9.81t^2=40

Divide both sides of the equation by $9.81$

\frac{9.81t^2}{9.81}=\frac{40}{9.81}

Simplify the fraction $\frac{9.81t^2}{9.81}$ by $9.81$

t^2=\frac{40}{9.81}

Divide both sides of the equation by $9.81$

t^2=\frac{40}{9.81}

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

\sqrt{t^2}=\sqrt{\frac{40}{9.81}}

Cancel exponents $2$ and $1$

t=\sqrt{\frac{40}{9.81}}

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

t=\sqrt{\frac{40}{9.81}}

The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$

t=\frac{\sqrt{40}}{\sqrt{9.81}}

The complete answer is

The time of the ball is

\frac{\sqrt{40}}{\sqrt{9.81}}

 Endgültige Antwort auf das Problem

The time of the ball is

\frac{\sqrt{40}}{\sqrt{9.81}}

Free Fall Rechner

Mit unserem Free Fall Schritt-für-Schritt-Rechner erhalten Sie detaillierte Lösungen für Ihre mathematischen Probleme. Üben Sie Ihre mathematischen Fähigkeiten und lernen Sie Schritt für Schritt mit unserem Mathe-Löser. Alle unsere Online-Rechner finden Sie hier.

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