Problem

6. A particle is projected vertically upwards from a point $A$ with speed $24\text{ m s}^{-1}$

The point $A$ is $2.5\text{ m}$ 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 $V\text{ m s}^{-1}$

After hitting the ground the particle does not rebound.

(a) Find the value of $V$.

(b) Find the time taken for the particle to reach $B$.

The point $C$ is $10\text{ m}$ vertically above $A$.

(c) Find the length of time for which the particle is above $C$.

(d) 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.)