A golf ball is hit from horizontal fairway ground towards a green that is guarded by a tall pine tree. The top of the tree is at a height of 4.50 m4.50\text{ m}4.50 m above the ground.
The ball is hit with an initial velocity of 24.0 m s−124.0\text{ m s}^{-1}24.0 m s−1 at an angle of 40.0∘40.0^\circ40.0∘ to the horizontal.
Air resistance is negligible and the golf ball can be treated as a projectile.
Show that the minimum speed of the golf ball during its flight is about 18 m s−118\text{ m s}^{-1}18 m s−1. Explain your answer.
The golf ball just clears the top of the tree at a time ttt after it is hit. Show that ttt satisfies the equation:
4.91t2−15.4t+4.50=0 4.91t^2 - 15.4t + 4.50 = 0 4.91t2−15.4t+4.50=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 ttt and discuss which of the two solutions is the time taken for the ball to clear the tree as it is descending. Explain the physical significance of the other solution.
A second attempt is made to hit the ball over the tree with the same initial velocity. This shot is played from a horizontal distance of 55.0 m55.0\text{ m}55.0 m from the tree. Deduce whether the ball can clear the tree.
