Step-by-step explanation:
Initial velocity = v at 37 degrees
Vertical POSITION = v sin (37) t - 1/2 (9.81) t^2 = 1.5
Horizontal position = v cos (37) t = 20 re-arrange to: t= 20/(v cos(37))
Use this value of 't' in the vertical POSITION equation to get
v sin (37) * 20/ ( v cos(37)) - 4.95 ( 20/(v cos(37))^2 ) = 1.5
now solve this mess for 'v' :
20 tan 37 = 1980/ ( v^2 cos(37)^2 ) + 1.5
13.571 = 3104.33 / v^2
v = 15.124 m/s and t = 1.656 s