3 A ball of mass 2 kg is moving with velocity \(( 3 \mathbf { i } - 2 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) when it is struck by a bat. The impulse on the ball is \(( - 8 \mathbf { i } + 10 \mathbf { j } )\) Ns.
- Find the speed of the ball immediately after the impact.
- State one modelling assumption you have used in answering part (a).
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\caption{Fig. 4}
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Fig. 4 shows a uniform lamina ABCDE such that ABDE is a rectangle and BCD is an isosceles triangle. \(\mathrm { AB } = 5 a , \mathrm { AE } = 4 a\) and \(\mathrm { BC } = \mathrm { CD }\). The point F is the midpoint of BD and \(\mathrm { FC } = a\). - Find, in terms of \(a\), the exact distance of the centre of mass of the lamina from AE.
The lamina is freely suspended from B and hangs in equilibrium.
- Find the angle between AB and the downward vertical.