A Gaelic football is kicked from horizontal ground towards the goalposts. The crossbar is at a height of 2.50 m above the ground.
The ball is kicked with an initial velocity of 18.0 m s-1 at an angle of 35.0∘ 35.0^\circ\,35.0∘ to the horizontal.
Air resistance is negligible and the ball can be treated as a projectile.
Show that the minimum speed of the ball during its flight is about 15 m s-1. Explain your answer.
The ball just passes over the crossbar at a time t t\,t after it is kicked. Show that t t\,t satisfies the equation:
4.91t2−10.3t+2.50=0 4.91t^2 - 10.3t + 2.50 = 0 4.91t2−10.3t+2.50=0(using g=9.81 m s−2g = 9.81\text{ m s}^{-2}g=9.81 m s−2).
Find the two solutions to this equation. State both values of t t\,t and discuss which of the two solutions is the time taken for the ball to pass over the crossbar from when it is kicked. Explain the physical significance of the other solution.
A second attempt is made to kick the ball over the crossbar with the same initial velocity. This kick is made from a horizontal distance of 29.0 m from the posts. Deduce whether the ball can pass over the crossbar.
