A uniform rod \(A B\), of mass 0.8 kg and length \(10 a\), is supported at the end \(A\) by a light inextensible vertical string and rests in limiting equilibrium on a rough fixed peg at \(C\), where \(A C = 7 a\).
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Two particles \(A\) and \(B\), of mass \(m\) and \(k m\) respectively, are moving in the same direction on a smooth horizontal surface. \(A\) has speed \(4 u\) and \(B\) has speed \(u\). The coefficient of restitution between \(A\) and \(B\) is \(e \quad A\) collides directly with \(B\), and in the collision the direction of \(A\) 's motion is reversed. Immediately after the impact, \(B\) has speed \(2 u\).
Show that the speed of \(A\) immediately after the impact is \(u ( 3 e - 2 )\).
Deduce the range of possible values of \(e\).
Show that \(4 < k \leq 5\).
A ball is projected from ground level with speed \(34 \mathrm {~ms} ^ { - 1 }\) at an angle \(\alpha\) above the horizontal, where \(\tan \alpha = \frac { 8 } { 15 }\).
Find the greatest height reached by the ball above ground level.
While it is descending, the ball hits a horizontal ledge 6 metres above ground level.
Find the horizontal distance travelled by the ball before it hits the ledge.
Find the speed of the ball at the instant when it hits the ledge.