At time \(t = 0\) seconds, a golf ball is hit from a point \(O\) on horizontal ground. The horizontal and vertical components of the initial velocity of the ball are \(3 U \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\) respectively. The ball hits the ground at the point \(A\), where \(O A = 120 \mathrm {~m}\). The ball is modelled as a particle moving freely under gravity.
Show that \(U = 14\)
Find the speed of the ball immediately before it hits the ground at \(A\).
Find the values of \(t\) when the ball is moving at an angle \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 1 } { 4 }\).