Final answer:
The question involves high school level physics, specifically projectile motion, requiring the calculation of initial velocity for a football to clear a 3-m-high goalpost at 45.7 m away. It also requires determining if the ball can be blocked by a lineman positioned at different distances.
Step-by-step explanation:
The subject of the question involves the physics of projectile motion often covered in high school classes. To determine the conditions under which a kicked football clears the goalposts, we must derive the maximum speed imparted to the ball by the kicker. Given that the angle of projection is 45° and the ball just clears a 3-m-high crossbar at a distance of 45.7 m away, we can use kinematic equations for uniform accelerated motion and the range equation for projectiles to find the necessary initial velocity.
For part (b), we calculate whether the football, with the already determined maximum initial velocity, will clear the lineman's reach when he is 4.6 m away, and then we determine the same for when he is just 1.0 m away, considering the lineman's vertical reach of 2.5 m.
The calculations involve breaking down the velocity into horizontal and vertical components and then using time of travel and maximum height reached to verify if the lineman can block the kick.