What is the direction of the change in velocity (Δv) when a basketball hits and rebounds from a backboard at a 45-degree angle?

When a basketball strikes a backboard at a 45-degree angle and subsequently rebounds, the direction of the change in velocity, denoted as Δv, is determined by analyzing the ball's velocity before and after the collision.

Upon hitting the backboard, the basketball initially has a velocity vector directed toward the backboard. After the rebound, the ball bounces back at an angle, which includes a significant upward component due to the angle of incidence affecting the angle of reflection. The change in velocity is defined as the final velocity minus the initial velocity.

Even though the physical motion involves both vertical and horizontal components, the key factor is that the basketball is reversing its horizontal component of motion. If the ball was approaching from the left side toward the backboard, this means after hitting the backboard and rebounding, its horizontal component of velocity would now be directed to the right. Thus, even if the basketball also has an upward motion after bouncing, the most significant aspect of the change in direction from the left to right constitutes a rightward change in velocity.

Therefore, the correct answer reflects that the direction of the change in velocity is rightward, as the velocity vector shifts from moving leftward to rightward after the collision with the backboard.