A particle $P$ is projected from a point $O$ at an angle of ${60^ \circ }$ above horizontal ground. At an instant $0.6{\text{ }}s$ after projection, the angle of elevation of $P$ from $O$ is ${45^ \circ }$ (see diagram).
a) Show that the speed of projection of $P$ is $8.20{\text{ }}m{\text{ }}{s^{ - 1}}$, correct to 3 significant figures.
b) Calculate the time after projection when the direction of motion of $P$ is ${45^ \circ }$ above the horizontal.

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