Learning Goal:

To analyze an oblique impact using the conservation of momentum and coefficient of restitution.

When an oblique impact occurs between two smooth particles, the particles move away from each other with velocity vectors that have unknown directions and unknown magnitudes. If the $y$ axis is within the plane of contact and the $x$ axis is the line of impact, the impulsive forces of deformation and restitution act only along the line of impact $($the $x$ axis$).$ Momentum of the system is conserved along the line of impact $($the $x$ axis$)$:

${\displaystyle \underset{?}{\overset{?}{}}}m(v_x{)}_1={\displaystyle \underset{?}{\overset{?}{}}}m(v_x{)}_2$

The coefficient of restitution, $e,$ relates the relativevelocity components of the particles along the line of impact $($the $x$ axis$)$:

Figure

$1$ of $2$

Part A

As shown, tennis ball A rolls off the top of a $10\mathrm{.}0$ m high wall, fall $4\mathrm{.}00$ m $,$ and strikes another tennis ball, $B,$ obliquely. $($Figure $1)$ Before the collision, tennis ball $B$ has a speed of $18\mathrm{.}0\frac{m}{s}$ as it moves upward. Each ball's mass is $57\mathrm{.}0$ g and the collision's coefficient of restitution is $0\mathrm{.}790.($Figure $2)$ In the figure, ${}_1=30\mathrm{.}0$ and ${}_1=20\mathrm{.}0.$ What is $(v_A{)}_1,$ the velocity of tennis ball $A,$ immediately before the collision?

Express your answer numerically in meters per second to three significant figures.

Vlew Avallable HInt$($s$)$

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Part B Complete previous part$($s$)$

Part C Complete previous part$($s$)$

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