Feynmann is wrong
The answer is 9/16

 

The change in velocity due to collision is only in the direction perpendicular to direction of collision.

Hence we can find a vector perpendicular to surface of collision by finding change in velocity.

Change in velocity is found by subtracting the velocity vectors:

(4i - j) - (i + 3j) = 3i - 4j

This vector is perpendicular to surface.

 

velocity perpendicular to surface before the collision:

(4i - j).(3i - 4j)/5 = 16/5

 

velocity perpendicular to surface after the collision:

(i + 3j).(3i - 4j)/5 = -9/5

 

e = 9/5 * 5/16 = 9/16