\(\mathbf { 1 }\) | \(\mathbf { 0 }\) A tennis ball is projected with velocity vector \(( 30 \mathbf { i } - 1 \cdot 4 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) from a point \(P\) which is at a height of 2.4 m vertically above a horizontal tennis court. The ball then passes over a net of height 0.9 m , before hitting the ground after \(\frac { 4 } { 7 } \mathrm {~s}\).
The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal and vertical respectively. The origin \(O\) lies on the ground directly below the point \(P\). The base of the net is \(x \mathrm {~m}\) from \(O\).
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a) Find the speed of the ball when it first hits the ground, giving your answer correct to one decimal place.
b) After \(\frac { 2 } { 5 } \mathrm {~s}\), the ball is directly above the net.
i) Find the position vector of the ball after \(\frac { 2 } { 5 } \mathrm {~s}\).
ii) Hence determine the value of \(x\) and show that the ball clears the net by approximately 16 cm .
c) In fact, the ball clears the net by only 4 cm .
i) Explain why the observed value is different from the value calculated in (b)(ii).
ii) Suggest a possible improvement to this model.