Answer:
Here, \[m=0.15kg,{{\upsilon
}_{i}}=54km/h=54\times \frac{5}{18}m{{s}^{-1}}=15m{{s}^{-1}}\]
\[{{\upsilon }_{\text{f}}}=\text{54
km}/\text{h }=\text{ 15m}{{\text{s}}^{\text{-1}}}\]
Impulse imparted to the ball
along X-axis
\[{{J}_{x}}\] = change in
momentum of ball along X-axis
\[=m{{\upsilon }_{fx}}-\left(
-m{{\upsilon }_{ix}} \right)=0.15\left( 15\cos {{45}^{o}}+15 \right)\]
\[=0.15\times 15\left[ \frac{1}{\sqrt{2}}+1
\right]=3.84kg\,m{{s}^{-1}}\].
Similarly, \[{{J}_{y}}=m{{\upsilon
}_{fy}}-m{{\upsilon }_{iy}}=0.15\left( 15\sin {{45}^{o}}-0
\right)=1.59kg\,m{{s}^{-1}}\]
Net impulse imparted to the
ball,
\[J=\sqrt{j_{x}^{2}+j_{y}^{2}}=\sqrt{{{3.84}^{2}}+{{1.59}^{2}}}=\sqrt{17.27}=4.16\,kg\,m{{s}^{-1}}\left(
or\,N-s \right)\]
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