4 A plane is inclined at an angle \(\theta ^ { \circ }\) to the horizontal. A particle is projected from a point A on the plane with speed \(V \mathrm {~ms} ^ { - 1 }\) in a direction making an angle of \(\phi ^ { \circ }\) with a line of greatest slope of the plane. The particle lands at a point B on the plane, as shown in the diagram, and the time of flight is \(T\) seconds.
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1. By considering the motion of the particle perpendicular to the plane, show that \(\mathrm { T } = \frac { 2 \mathrm {~V} \sin \phi } { \mathrm {~g} \cos \theta }\). Consider the case when \(\theta = 30 , \phi = 25\) and \(V = 20\).
2. 1. Calculate the distance AB .
   2. State, with reasons but without any detailed calculations, what effect each of the following actions would have on the distance AB .
      • Increasing \(V\) while leaving \(\theta\) and \(\phi\) unchanged.
3. Increasing \(\phi\) while leaving \(\theta\) and \(V\) unchanged.