8 In this question the value of \(\boldsymbol { g \) should be taken as \(\mathbf { 1 0 } \mathbf { m ~ s } ^ { \mathbf { - 2 } }\).}
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]{52d6c914-b204-4587-a82e-fbab6693fcf8-6_476_1111_518_475}
\captionsetup{labelformat=empty}
\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.