To determine the maximum time allowed for calculations between the three pictures being taken and the robot commencing motion, we need to consider the time it takes for the ball to cross the net and reach the robot's optimal location.
Let's analyze the scenario step by step:
1. Ball crossing the net:
The net is located 140 cm from each side, so the distance the ball needs to travel before crossing the net is \(280 \, \text{cm} - 140 \, \text{cm} = 140 \, \text{cm}\).
The maximum speed of the ball is given as 20 miles per hour. Let's convert this speed to centimeters per second:
\(20 \, \text{miles/hour} = 20 \times 1609.34 \, \text{cm/hour} \approx 32,187 \, \text{cm/hour} \approx 8.94 \, \text{cm/second}\).
Therefore, the time it takes for the ball to cross the net is \(140 \, \text{cm} / 8.94 \, \text{cm/second} \approx 15.67 \, \text{seconds}\).
2. Robot's movement:
The robot can move side to side with a velocity of 1000 cm/s. To reach the optimal position, the robot needs to cover a distance of either 150 cm or 130 cm, depending on its initial position.
The maximum time it takes for the robot to move to either side is \(150 \, \text{cm} / 1000 \, \text{cm/second} = 0.15 \, \text{seconds}\).
3. Calculations time:
The maximum time allowed for calculations is the time remaining after subtracting the time for the ball to cross the net and the time for the robot's movement from the total time available.
Total time available: 15.67 seconds
Time for ball crossing the net: 15.67 seconds
Time for robot's movement: 0.15 seconds
Calculations time = Total time available - Time for ball crossing the net - Time for robot's movement.
Calculations time = 15.67 seconds - 15.67 seconds - 0.15 seconds = 0.85 seconds.
Therefore, the maximum time allowed for calculations between the three pictures being taken and the robot commencing motion is approximately 0.85 seconds.