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 Difficult Problems

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

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

$v_0^2=62.784$
11

Removing the variable's exponent

$\left(v_0^2\right)^{0.5}=62.784^{0.5}$
12

Calculate the power $62.784^{0.5}$

$\left(v_0^2\right)^{0.5}=7.9236$

Simplify $\left(v_0^2\right)^{0.5}$ 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 $0.5$

$v_0^{2\cdot 0.5}=7.9236355$

Multiply $2$ times $0.5$

$v_0^{1}=7.9236$

Any expression to the power of $1$ is equal to that same expression

$v_0=7.9236$
13

Simplify $\left(v_0^2\right)^{0.5}$ 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 $0.5$

$v_0=7.9236$
14

The speed of the stone is $7.9236$ m/s
The speed of the stone is $7.9236$ m/s