Answer
$v_i=21 m/s$
Work Step by Step
We can find the required velocity as follows:
$v_i=\sqrt{\frac{g(\Delta x)^2}{2cos^2\theta (\Delta x tan \theta-\Delta y)}}$
We plug in the known values to obtain:
$v_i=\sqrt{\frac{(9.8)(50)^2}{2cos^2 53^{\circ}[50 tan53^{\circ} -(-12)]}}$
This simplifies to:
$v_i=21 m/s$
