M2 June 2015 Q7

EdexcelOld spec12 marksProjectiles

7.

Figure 3: particle projected from O at u m/s at theta degrees, passing through A moving at 15 m/s at 20 degrees above the horizontal, landing at C
Figure 3

At time \(t = 0\), a particle is projected from a fixed point \(O\) on horizontal ground with speed \(u\) m s\(^{-1}\) at an angle \(\theta^\circ\) to the horizontal. The particle moves freely under gravity and passes through the point \(A\) when \(t = 4\) s. As it passes through \(A\), the particle is moving upwards at 20\(^\circ\) to the horizontal with speed 15 m s\(^{-1}\), as shown in Figure 3.

(a) Find the value of \(u\) and the value of \(\theta\). (7)

At the point \(B\) on its path the particle is moving downwards at 20\(^\circ\) to the horizontal with speed 15 m s\(^{-1}\).

(b) Find the time taken for the particle to move from \(A\) to \(B\). (2)

The particle reaches the ground at the point \(C\).

(c) Find the distance \(OC\). (3)
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