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Question: You have been tasked with building a robot that plays table tennis (i.e., ping pong). A ping pong table is 280 cm in length and is 150 cm wide. There is a net stretched across the center of the table, 140cm in from each side. The robot can move side to side with a velocity of 1000 cm/s.
The robot works by capturing 3 pictures of the ball in motion; these 3 pictures all should be taken before the ball breaks the plane of the net, which is halfway across the table. It then will process the images and determine the optimal location that it must be to hit the ball. It is possible that that optimal location may be all the way to the left or all the way to the right of the 150 cm side.
Given that all 3 pictures must be captured, and the physics of the movement of the robot (you may assume it can instantaneously change from 0 to 1000 cm/s of velocity, and a maximum ping pong ball speed of 20 miles per hour, how long can the calculations be between the 3 pictures being taken and the robot commencing motion if it is guaranteed to hit the ball? In solving this problem, sketch your solution and show your calculations.
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