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A projectile is launched at time \( t=0 \) from point \( A \) which is at height \( 1 \mathrm{~m} \) above the floor with speed \( v \mathrm{~m} \mathrm{~s}^{-1} \) and at an angle \( \theta=45^{\circ} \) with the floor. It passes through a hoop at \( B \) which is \( 1 \mathrm{~m} \) above \( A \) and \( B \) is the highest point of the trajectory. The horizontal distance between \( A \) and \( B \) is \( d \) meters. The projectile then falls into a basket, hitting the floor at \( C \) a horizontal distance \( 3 d \) meters from \( A \). Find \( l \) (in m).
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