question_answer

A batsman deflects a ball by an angle of \[{{45}^{o}}\] without changing its initial speed which is equal to\[\text{54 km }{{\text{h}}^{-1}}\]. What is the impulse imparted to the ball? Mass of the ball is 0-15 kg.

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,                                  \[J=\sqrt{j_{x}^{2}+j_{y}^{2}}=\sqrt{{{3.84}^{2}}+{{1.59}^{2}}}=\sqrt{17.27}=4.16\,kg\,m{{s}^{-1}}\left( or\,N-s \right)\]