9231 P33 - Jun 2024 - Q6 - 8 marks
6918
A particle \(P\) is projected with speed \(u\,\text{m s}^{-1}\) at an angle \(\theta\) above the horizontal from a point \(O\), and moves freely under gravity.
After \(5\) seconds the speed of \(P\) is \(\dfrac34u\).
(a) Show that
\(\frac{7}{16}u^2-100u\sin\theta+2500=0.\)
(b) It is given that the velocity of \(P\) after \(5\) seconds is perpendicular to the initial velocity. Find, in either order, \(u\) and \(\sin\theta\).
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