Pinball with velocity vector

[WMDhamnekar]

Hi,

A pinball moving in a plane with velocity s bounces (in a purely elastic impact) from a baffle whose endpoints are p and q. What is the velocity vector after the bounce?

I don't understand how to answer this question? Any math help, hint or even correct answer will be accepted?

 

[DaalChawal]

Use vectors addition and elastic collision concept that velocity along the baffle will remain unchanged and velocity perpendicular to baffle will get reversed.

 

[HOI]

You can always set up a coordinate with P as origin and Q= (0, 1). The velocity vector of this object can be written $(v_x, v_y)$ in that coordinate system. After an elastic collision with PQ, it's velocity vector is $(-v_x, v_y)$.

 

[WMDhamnekar]

You can always set up a coordinate with P as origin and Q= (0, 1). The velocity vector of this object can be written $(v_x, v_y)$ in that coordinate system. After an elastic collision with PQ, it's velocity vector is $(-v_x, v_y)$.

Hi,

Author has given the following answer to this question. Would you tell me how does the highlighted terms relate to velocity before and after the bounce?

 

[DaalChawal]

A vector $u = u_x + u_y $ you can write a vector as a sum of its components.
$(s. \hat{u} ) $ represents the magnitude of the component of vector s along baffle and if you multiply by unit vector $\hat{u}$ you get vector component of s along with the baffle similarly $(s. \hat{v})$ represents the magnitude of the component of vector s normal to baffle and again if you multiply by unit vector $\hat{v}$ you will get vector component of s normal to baffle.
For reflected ray normal gets reversed so the normal vector is expressed with the negative sign there.