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1 year ago

The kinetic energy(Jules) of an object can be calculated using the following formula:

Mathematics

1 answer:

weeeeeb [17]1 year ago

3 0

Answer:

75 J

Step-by-step explanation:

You want to know the kinetic energy in joules of a 6 kg ball that has a velocity of 5 m/s. The formula is given.

<h3>Kinetic energy</h3>

Kinetic energy is energy of motion. It is jointly proportional to mass and the square of velocity. The value is given by the formula ...

KE = 1/2·mv²

For the given values of mass (6 kg) and velocity (5 m/s), the kinetic energy is ...

$KE=\dfrac{1}{2}(6\text{ kg})(5\text{ m/s})^2=75\text{ kg$\cdot$m$^2$/s$^2$}=\boxed{75\text{ J}}$

The kinetic energy of the ball is 75 joules.

<em>Additional comment</em>

The unit joule (J) is a derived unit of energy equal to 1 kg·m²/s²

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If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

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2 years ago

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Sphinxa [80]

Answer:-

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Step-by-step explanation:

x+2/3=-1/6

after cross-mutiplying,

6(x+2)=-3

6x+12=-3

6x=-3-12

6x=-15

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hope this helps u!!

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