A man loses $20 \%$ of his velocity after running through $108 \mathrm{~m}$. Find maximum distance he can run. Further, if his retardation is uniform.

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Aicharya · Accepted Answer

Let the initial velocity be $u$. Since the man loss $20 \%$ of his velocity after running through $108 \mathrm{~m}$, Hence, velocity at this mos Now, initial velocity $=u$ Final velocity $=0.8 u$ and $s=108 \mathrm{~m} ; a=?$ Final velocity $=0.8 u$ and $s=108 \mathrm{~m} ; a=?$ Using $v^{2}=u^{2}+2 a s \Rightarrow(0.8 u)^{2}=u^{2}+2 a .(108)$ $216 a=0.64 u^{2}-u^{2}=-0.36 u^{2} \Rightarrow a=-\frac{0.36}{216} u^{2}=-\frac{1}{600} u^{2}$ Now, let the man run a further distance of $x \mathrm{~m}$. In second segment of his motion: Initial velocity $=0.8 u$, final velocity $=0 ; s=x$; Again using $v^{2}=u^{2}+2 a . s \Rightarrow 0=(0.8 u)^{2}+2 a x$ $\begin{aligned} 0 &=0.64 u^{2}+2\left(-\frac{1}{600} u^{2}\right) x \Rightarrow\left(\frac{1}{300} u^{2}\right) x=0.64 u^{2} \ \Rightarrow x &=0.64 \times 300=192 \mathrm{~m} \end{aligned}$ ,

A man loses \(20 \%\) of his velocity after running through \(108 \mathrm{~m}\). Find maximum distance he…

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