3 A particle is projected vertically upwards, from the ground, with a speed of \(28 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Ignoring air resistance, find
- the maximum height reached by the particle,
- the speed of the particle when it is 30 m above the ground,
- the time taken for the particle to fall from its highest point to a height of 30 m ,
- the length of time for which the particle is more than 30 m above the ground.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{463347e9-b850-4f4a-b2d2-423cf142e30f-3_569_1132_258_516}
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\caption{Fig. 1}
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A woman runs from \(A\) to \(B\), then from \(B\) to \(A\) and then from \(A\) to \(B\) again, on a straight track, taking 90 s . The woman runs at a constant speed throughout. Fig. 1 shows the \(( t , v )\) graph for the woman. - Find the total distance run by the woman.
- Find the distance of the woman from \(A\) when \(t = 50\) and when \(t = 80\),
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{463347e9-b850-4f4a-b2d2-423cf142e30f-3_424_1135_1233_513}
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\caption{Fig. 2}
\end{figure}
At time \(t = 0\), a child also starts to move, from \(A\), along \(A B\). The child walks at a constant speed for the first 50 s and then at an increasing speed for the next 40 s . Fig. 2 shows the ( \(t , v\) ) graph for the child; it consists of two straight line segments. - At time \(t = 50\), the woman and the child pass each other, moving in opposite directions. Find the speed of the child during the first 50 s .
- At time \(t = 80\), the woman overtakes the child. Find the speed of the child at this instant.