2 In this question the value of \(g\) should be taken as \(10 \mathrm {~m \mathrm {~s} ^ { 2 }\).}
As shown in Fig. 8, particles A and B are projected towards one another. Each particle has an initial speed of \(10 \mathrm {~m} \mathrm {~s} ^ { 1 }\) vertically and \(20 \mathrm {~m} \mathrm {~s} { } ^ { 1 }\) horizontally. Initially A and B are 70 m apart horizontally and B is 15 m higher than A . Both particles are projected over horizontal ground.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{362d5995-bd39-4b07-b6a4-63eb1dd3e69d-2_461_1114_464_505}
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\caption{Fig. 8}
\end{figure}
- Show that, \(t\) seconds after projection, the height in metres of each particle above its point of projection is \(10 t - 5 t ^ { 2 }\).
- Calculate the horizontal range of A . Deduce that A hits the horizontal ground between the initial positions of A and B .
- Calculate the horizontal distance travelled by B before reaching the ground.
- Show that the paths of the particles cross but that the particles do not collide if they are projected at the same time.
In fact, particle A is projected 2 seconds after particle B .
- Verify that the particles collide 0.75 seconds after A is projected.