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Esempio

Problemi risolti

Problemi difficili

1

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

With what speed should a stone be thrown upward so that it reaches a maximum height of 3.2 m?
2

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

$a=9.81\:m/s2,\:\: v=0,\:\: y=3.2\:m,\:\: y_0=0,\:\: v_0=\:?$
3

According to the initial data we have about the problem, the following formula would be the most useful to find the unknown ($v_0$) that we are looking for. We need to solve the equation below for $v_0$

$v^2=v_0^2-2a\left(y- y_0\right)$
4

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

$0^2=v_0^2-2\cdot 9.81\left(3.2- 0\right)$
5

Add the values $3.2$ and $0$

$0^2=v_0^2-2\cdot 9.81\cdot 3.2$
6

Multiply $-2$ times $9.81$

$0^2=v_0^2-19.62\cdot 3.2$
7

Multiply $-19.62$ times $3.2$

$0^2=v_0^2-62.784$
8

Calculate the power $0^2$

$0=v_0^2-62.784$
9

Rearrange the equation

$v_0^2-62.784=0$
10

We need to isolate the dependent variable $v_0$, we can do that by simultaneously subtracting $-62.784$ from both sides of the equation

$v_0^2=62.784$

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

$\sqrt{v_0^2}=\sqrt{62.784}$

Cancel exponents $2$ and $1$

$v_0=\sqrt{62.784}$

Calculate the power $\sqrt{62.784}$

$v_0=7.9236$
11

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

$v_0=7.9236$
12

The complete answer is

The speed of the stone is $7.9236355$ m/s

Risposta finale al problema

The speed of the stone is $7.9236355$ m/s

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