Final answer:
The final velocity of the ball after colliding with the wall will be -1 m/s in the x-direction (due to the coefficient of restitution being half) and the same 2 m/s in the y-direction (as it remains unchanged), resulting in a velocity of -i + 2j.
Step-by-step explanation:
The question involves a ball moving on a horizontal surface and experiencing a collision with a wall. The coefficient of restitution (c) is a measure of the elasticity of the collision and is given as half in this scenario. A perfectly elastic collision has a c of 1, meaning there is no loss of kinetic energy.
In this case, the coefficient of restitution being half indicates that the ball will rebound with half the speed it had before collision in the direction perpendicular to the wall. If the ball's initial velocity components in the x and y directions are 2i and 2j respectively (which means 2 m/s to the right and 2 m/s upwards), after the collision, the velocity component perpendicular to the wall (x-direction) will reverse and be halved due to the coefficient of restitution, becoming -1 m/s. The y-component (parallel to the wall) will remain unchanged. Thus, the final velocity of the ball just after it hits the wall will be -i + 2j (or -1 m/s in the x-direction and 2 m/s in the y-direction).