1. A particle is projected vertically upwards from a point \(A\) with speed \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\)

The point \(A\) is 2.5 m vertically above the point \(B\).
Point \(B\) lies on horizontal ground.
The particle moves freely under gravity until it hits the ground at \(B\) with speed \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\) After hitting the ground the particle does not rebound.

1. Find the value of \(V\).
2. Find the time taken for the particle to reach \(B\). The point \(C\) is 10 m vertically above \(A\).
3. Find the length of time for which the particle is above \(C\).
4. Sketch a speed-time graph for the motion of the particle from projection to the instant that it reaches \(B\). (No further calculations are required.)