A small sphere of mass \( m=1 \mathrm{~kg} \) is moving with a velocity \( (4 \hat{i}-\hat{j}) \...

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A small sphere of mass \( m=1 \mathrm{~kg} \) is moving with a velocity \( (4 \hat{i}-\hat{j}) \mathrm{m} / \mathrm{s} \). It hits a fixed smooth wall and rebounds with velocity \( (\hat{i}+3 \hat{j}) \mathrm{m} / \mathrm{s} \). The coefficient of restitution between the sphere and the wall is \( n / 16 \). Find the value of \( n \).
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