# A 23.0 g ball is fired horizontally with initial speed

A 23.0 g ball is fired horizontally with initial speed v0 toward a 110 g ball that is hanging motionless from a 1.00 m -long string. The balls undergo a head-on, perfectly elastic collision, after which the 110 g ball swings out to a maximum angle ${\theta }_{max}={51.0}^{\circ }$
What was ${v}_{0}$?
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servidopolisxv
The expression of the initial speed from conservation of energy,
$KE=PE$
$\frac{1}{2}{m}_{b1}{v}_{0}^{2}={m}_{b2}gh$
$\frac{1}{2}{m}_{b1}{v}_{0}^{2}={m}_{b2}gl\left(1-\mathrm{cos}\theta \right)$
${v}_{0}=\sqrt{\frac{2{m}_{b2}gl\left(1-\mathrm{cos}\theta \right)}{{m}_{b1}}}$
Substitute the values,