Final answer:
The change in velocity when a tennis ball is thrown towards a wall is the difference between its initial and final velocity considering direction. For a ball striking a wall at an angle and bouncing off at the same speed and angle, the impulse delivered can be represented as the change in momentum, factoring in mass and velocity components. To calculate the resultant displacement of a ball rolling towards and then away from a wall, combine the distance covered before and after striking the wall.
Step-by-step explanation:
The change in velocity of a tennis ball thrown towards a wall can be calculated by finding the difference between its initial and final velocity, taking into account both magnitude and direction.
Change in Velocity Example:
Suppose a tennis ball is thrown horizontally at an initial velocity of 3 m/s towards a wall. After striking the wall, the ball returns at 2 m/s. To determine the change in velocity (Δv), we need to consider that the ball's direction changed 180 degrees. The initial and final velocities are vectors, and since the ball is moving in the opposite direction after striking the wall, the final velocity will be negative relative to the initial direction. Therefore, the change in velocity is Δv = vf - vi = -2 m/s - 3 m/s = -5 m/s. However, when considering the magnitude, the change is 5 m/s.
For the impulse delivered by the wall when a ball at an angle strikes it, we need to consider both the x (horizontal) and y (vertical) components of the motion. Since the speed remains the same and the ball bounces off at the same angle, only the horizontal direction changes. However, as impulse is a vector quantity, and this problem involves an angle, it is more complex and requires understanding vector components of the impulse. To solve it, we would use the formula Impulse J = Change in momentum = m * Δv. Without the mass of the ball, we're unable to provide a numeric answer, but the change in momentum can be represented by two times the horizontal component of the initial velocity times the mass, due to the change in direction of the velocity and it's constant magnitude in that direction.
Calculating Resultant Displacement:
To calculate the resultant displacement of a tennis ball that is rolled towards a wall and then rolls away, we take the initial path towards the wall (10 m) and the path after the collision (2.5 m) and find the algebraic sum which would be 10 m + 2.5 m = 12.5 m.