A ball is thrown with initial velocity 20 m/s at an angle of elevation of arctan (4/3). Suppose that the ball is thrown up a road inclined at arctan(1/5) to the horizontal. Show that the ball si about 9 m above the road when it reaches its greatest height and the time of flight is 2.72 seconds, and find, correct to the nearest tenth of a metre, the distance the ball has been thrown up the road.

I've already found out from previous parts that:

* the parabolic path of the ball has parametric equationx x=12t and y=16t-5t^2

* the horizontal range of the ball is 38.4 m

* the greatest height is 12.8 m