Physics, asked by jasminder8413, 1 year ago

If a man increases his speed by 2m/s, his K.E. is doubled. What is the original speed of man?

Answers

Answered by ksharan011
57
solve further by using Quadratic formula, and u will have the required answer..
hope it helps you.
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Answered by MOSFET01
39
 \huge {\green{\underline{Solution}}}

Let we consider it's original speed = x m/sec

and second speed be y m/sec

y = x+2 m/sec

 Kinetic \: Energy = \frac{1}{2}m v^{2}

Takes equation first

 \red{KE_1 = \frac{1}{2}mx^{2}}...eq(1)

Takes equation second

 \red{2KE_2 = \frac{1}{2} m(x+2)^{2}}...eq(2)

\blue{\boxed{KE_2 = 2 KE_1}}

Divide both equation

\orange{\boxed{ \frac{KE_1}{2KE_1} = \frac{ \frac{1}{2} mx^{2}}{\frac{1}{2} m(x^{2}+4+4x)}}}\\\\\frac{1}{2} = \frac{x^{2}}{x^{2}+4+4x}\\ 2x^{2} = x^{2}+4+4x\\2x^{2}-x^{2}-4-4x = 0\\x^{2}-4-4x = 0

 x= \frac{-b+\sqrt{b^{2}-4ac}}{2a}

or

 x=\frac{-b -\sqrt{b^{2}-4ac}}{2a}

 x=\frac{-(-4) +\sqrt{4-4\times1\times -4}}{2\times 1}\\x=\frac{4+\sqrt{16+16}}{2}\\x=\frac{4 + \sqrt32 }{2}\\x = \frac{<br />\cancel 2(2 + 2\sqrt{2})}{\cancel{2}}\\x = 2+ 2\sqrt2

 x=\frac{-(-4) - \sqrt{(-4)^{2}-4\times1\times -4}}{2\times 1}\\x=\frac{4-\sqrt{16+16}}{2}\\x=\frac{4 -\sqrt32 }{2}\\x = \frac{\cancel 2(2 +2\sqrt{2})}{\cancel{2}}\\x = 2-2\sqrt2

 \red{\boxed{x = 2+2\sqrt2 \:or \:2-2\sqrt2}}
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