6. A particle \(P\) is projected from a point \(A\) on horizontal ground with speed \(u\) at an angle of elevation \(\alpha\) and moves freely under gravity. \(P\) hits the ground at the point \(B\).
- Show that \(A B = \frac { u ^ { 2 } } { g } \sin 2 \alpha\).
An archer fires an arrow with an initial speed of \(45 \mathrm {~ms} ^ { - 1 }\) at a target which is level with the point of projection and at a distance of 80 m .
Given that the arrow hits the target,
- find in degrees, correct to 1 decimal place, the two possible angles of projection.
- Write down, with a reason, which of the two possible angles of projection would give the shortest time of flight.
(2 marks) - Show that the minimum time of flight is 1.8 seconds, correct to 1 decimal place.
(2 marks)