Question: A (20 mathrm{~g}) ball is fired horizontally with initial speed (v_{mathrm{i}}) toward a (100 mathrm{~g}) ball that is hanging motionless from a (1.0-mathrm{m})-long string. The

A $20 \mathrm{~g}$ ball is fired horizontally with initial speed $v_{\mathrm{i}}$ toward a $100 \mathrm{~g}$ ball that is hanging motionless from a $1.0-\mathrm{m}$-long string. The balls undergo a head-on, perfectly elastic collision, after which the $100 \mathrm{~g}$ ball swings out to a maximum angle $\theta_{\max }=50^{\circ}$. What was $v_{\mathrm{i}}$ ?

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