(a) To find the maximum speed the kicker can impart to the football, we can use the range equation for projectile motion. The range (R) is given as 45.7 m, the initial angle (θ) is 45°, and the vertical displacement (Δy) is 3 m.
The range equation is given by:
R = (v^2 * sin(2θ)) / g
Rearranging the equation to solve for v (the maximum speed), we have:
v = sqrt((R * g) / sin(2θ))
Plugging in the values, we get:
v = sqrt((45.7 m * 9.8 m/s^2) / sin(90°))
v ≈ 25.1 m/s
Therefore, the maximum speed the kicker can impart to the football is approximately 25.1 m/s.
(b) To determine if the lineman can block the field goal attempt, we need to calculate the maximum height (H) reached by the football. We can use the following equation for the vertical displacement:
Δy = (v^2 * sin^2(θ)) / (2g)
Plugging in the values, we get:
Δy = (25.1 m/s)^2 * sin^2(45°) / (2 * 9.8 m/s^2)
Δy ≈ 5.1 m
Since the maximum height reached by the football is 5.1 m, and the lineman has a vertical reach of 2.5 m, the lineman cannot block the field goal attempt.
(c) If the lineman is 1.0 m away, it does not affect the ability to block the field goal attempt since the vertical reach of the lineman is still less than the maximum height reached by the football (5.1 m). Therefore, the lineman cannot block the field goal attempt even if they are 1.0 m away.