6 A particle \(P\) is projected with speed \(u \mathrm {~ms} ^ { - 1 }\) at an angle \(\theta\) above the horizontal from a point \(O\) and moves freely under gravity. After 5 seconds the speed of \(P\) is \(\frac { 3 } { 4 } u\).

1. Show that \(\frac { 7 } { 16 } u ^ { 2 } - 100 u \sin \theta + 2500 = 0\).
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2. It is given that the velocity of \(P\) after 5 seconds is perpendicular to the initial velocity. Find, in either order, the value of \(u\) and the value of \(\sin \theta\).