Determining Initial Conditions from Position or Flight Data

The question provides position at a given time, times at which the projectile is at the same height, or other flight data and asks to determine initial speed, launch angle, or initial velocity components.

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A projectile fired at $30^\circ$ to the ground is observed to be at same height at time 3 s and 5 s after projection, during its flight. The speed of projection of the projectile is $\_\_\_\_$ $\mathrm{m}\mathrm{~s}^{-1}$. (Given $g = 10$ m s$^{-2}$)