In Madden 14 (football video game) when punting you sometimes face adverse weather
conditions. Does the angle in which you choose to make your punt matter?
Assume the following conditions: The average Madden punter can kick a ball at 40
km/h and there is on average a head wind of 20 km/h.
Task: Determine the process your gaming system uses to determine what angle
allows the punter to kick the ball so it travels the farthest distance.
To determine the angle that allows the punter to kick the ball so it travels the farthest distance, you should consider the following process:
1. Calculate the resultant velocity: In this case, the punter's kick speed is 40 km/h, and there is a headwind of 20 km/h. To find the resultant velocity, you need to consider both the kick speed and the wind speed. Since the headwind is opposite to the direction of the kick, you subtract the wind speed from the kick speed. In this case, the resultant velocity would be 40 km/h - 20 km/h = 20 km/h.
2. Decompose the resultant velocity: Since we want to find the angle that allows the ball to travel the farthest distance, we need to decompose the resultant velocity into its horizontal and vertical components. The horizontal component represents the distance covered by the ball, while the vertical component represents how high the ball goes.
3. Calculate the time of flight: The time of flight is the total time the ball is in the air. To calculate this, you need to use the vertical component of the resultant velocity and the acceleration due to gravity. In this case, the vertical component is zero because we want the ball to travel along the ground. Therefore, the time of flight would be zero.
4. Calculate the range: The range is the horizontal distance covered by the ball. To calculate this, you use the horizontal component of the resultant velocity and the time of flight. In this case, the horizontal component is 20 km/h and the time of flight is 0, so the range would be zero.
5. Repeat the process for different angles: To find the angle that allows the ball to travel the farthest distance, you need to repeat this process for various angles. Calculate the resultant velocity for each angle, decompose it into horizontal and vertical components, calculate the time of flight, and determine the range. By comparing the ranges for different angles, you can find the angle that gives the maximum distance.
By following this process and testing different angles, your gaming system should be able to determine the angle that allows the punter to kick the ball so it travels the farthest distance in adverse weather conditions in Madden 14.