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Pinball with velocity vector

Dhamnekar Winod

Active member
Nov 17, 2018
163
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

Member
Apr 8, 2021
89
Use vectors addition and elastic collision concept that velocity along the baffle will remain unchanged and velocity perpendicular to baffle will get reversed.
 

Country Boy

Well-known member
MHB Math Helper
Jan 30, 2018
821
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 $(-v_x, v_y)$.
 

Dhamnekar Winod

Active member
Nov 17, 2018
163
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?

1624939118433.png
 

DaalChawal

Member
Apr 8, 2021
89
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.