Answer:
0 degrees off center.
Explanation:
To determine the degree off center and the overall speed of the ping pong ball, we need to consider the vector addition of the ball's velocity due to smashing and the velocity due to the crosswind. Let's break down the problem step by step:
Calculate the horizontal and vertical components of the ball's velocity due to smashing:
The initial velocity of the ball due to smashing is 60.0 km/h. Since the ball is smashed straight down the center line of the table, the vertical component of the velocity is 0 km/h, and the horizontal component is 60.0 km/h.
Calculate the horizontal and vertical components of the ball's velocity due to the crosswind:
The crosswind velocity is 25.0 km/h, and since it sweeps across the table parallel to the net, it only affects the horizontal component of the ball's velocity. Therefore, the horizontal component of the ball's velocity due to the crosswind is 25.0 km/h.
Determine the resultant horizontal and vertical velocities:
To find the overall horizontal velocity, we need to add the horizontal components of the velocities due to smashing and the crosswind:
Overall horizontal velocity = smashing horizontal velocity + crosswind horizontal velocity
Overall horizontal velocity = 60.0 km/h + 25.0 km/h = 85.0 km/h
Since the vertical component of the velocity due to smashing is 0 km/h and the crosswind does not affect the vertical component, the overall vertical velocity remains 0 km/h.
Calculate the resultant speed and direction:
To find the resultant speed, we can use the Pythagorean theorem:
Resultant speed = √(horizontal velocity^2 + vertical velocity^2)
Resultant speed = √(85.0 km/h)^2 + (0 km/h)^2) = √(7225 km^2/h^2) = 85.0 km/h
The ball ends up with an overall speed of 85.0 km/h.
Since the vertical velocity remains 0 km/h, the ball will not deviate vertically from the center line. Therefore, the ball will end up at the same height as the center line.
To determine the degree off center, we can calculate the angle of the resultant velocity using trigonometry:
Angle off center = arctan(vertical velocity / horizontal velocity)
Angle off center = arctan(0 km/h / 85.0 km/h) = arctan(0) = 0°
The ball will not deviate horizontally from the center line, resulting in 0 degrees off center.