Final answer:
Using physics principles, we first determine the correct throwing angle for the quarterback, and then calculate the initial kicking speed and the ability of a lineman to block a field goal, all based on projectile motion and kinematics.
Step-by-step explanation:
To answer this physics problem, we need to analyze the motion of the football and its trajectory in order to determine if the receiver can catch the ball. Additionally, for the field goal question, we must calculate the football's flight path to see if it clears the crossbar and whether it can be blocked by the onrushing defensive lineman.
For the receiver to catch the football thrown by Aaron, we need to calculate the angle at which Aaron must throw the ball, taking into consideration the receiver's speed and the distance the ball needs to travel. This involves understanding projectile motion and using equations that take into account initial speed, velocity, and the effect of gravity. As for the field goal problem, the initial speed of the football when kicked at a 45° angle must be calculated to ensure it clears the crossbar, and we must assess whether the lineman can block the kick, using his distance from the kicker and his jump reach.