a football player attempts a field goal from a distance of 52 yards. The ball reaches a maxium height of 9 yrds and lands 8 yards behind the uprights. If the uprights are 3 yards high. algebraically determine if the field goal was successful
To determine if the field goal was successful, we need to determine whether the ball cleared the uprights or not.
Let's consider the path of the ball when it is kicked. From the given information, we know that the ball reaches a maximum height of 9 yards. This means that at the highest point of its trajectory, the vertical distance from the ground is 9 yards.
Now, let's analyze the horizontal distance traveled by the ball. We are told that the ball lands 8 yards behind the uprights. To determine the total horizontal distance traveled, we need to find the distance from the point of landing to the uprights themselves.
Since the distance from the point of landing to the uprights is 8 yards, and the distance from the uprights to the ground is 3 yards, we can calculate the total horizontal distance traveled by the ball as:
Total horizontal distance = 8 + 3 = 11 yards
Now, we have the vertical and horizontal distances traveled by the ball. To determine if the field goal was successful, we need to check if the ball cleared the uprights.
The height of the uprights is 3 yards, and the maximum height of the ball's trajectory is 9 yards. So, to clear the uprights, the ball needs to be at least 3 yards higher than the height of the uprights when it passes them.
Since the ball reaches a maximum height of 9 yards, which is higher than the 3-yard height of the uprights, we can conclude that the ball cleared the uprights.
Therefore, the field goal was successful.