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Question

**Oblique Impact**

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):

∑*m*(**v***x*)1=∑*m*(**v***x*)2

The coefficient of restitution, *e*, relates the relative-velocity components of the particles along the line of impact (the *x* axis):

*e*=(**v***Bx*)2−(**v***Ax*)2(**v***Ax*)1−(**v***Bx*)1

The momenta of both particles *A* and *B* are conserved in the plane of contact (the *y* axis) because no impulse acts on either particle in this plane. Therefore, the *y* component of the velocities before and after the collisions remains unchanged:

(**v***y*)1=(**v***y*)2

As shown, tennis ball *A* rolls off the top of a 10.0 m high wall, falls 4.00 m, and strikes another tennis ball, *B*, obliquely. (Figure 1) Before the collision, tennis ball *B* has a speed of 23.0 m/s as it moves upward. Each ball's mass is 57.0 g and the collision's coefficient of restitution is 0.630. (Figure 2) In the figure, *θ*1=30.0∘ and *ϕ*1=20.0∘. What is (**v***A*)1, the velocity of tennis ball *A*, immediately before the collision?

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Engineering

Mechanical Engineering

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Transcribed Image Text

A. 4 m L-L-LH И1 L-L L-L L-L-LFL-L-L

A в, |(VA)ı (VA)2 plane of (VB)1 ф2 contact (Ув)2 Фт line of impact- X.