Question

what minimum initial velocity must aprojectile have to reach atarget at a distance of 25m away? (g: 10m/s)

Answer 1

do you know max range is 45 degrees above horizontal ? If so
speed S
u = horizontal speed = s cos 45
Vi = initial vertical speed = S sin 45

time in air = 25/u
half time in air = time rising = 12.5/u = t

v = Vi - 10 t
v = 0 at top of rise phase
so
Vi = 10 t
Vi = 10 (12.5/u)
S sin 45 = 125 /S cos 45

S^2 sin 45 cos 45 = 125
but sin 45 = cos 45 = sqrt 2/2
so
S^2 (1/2)= 125
S = sqrt 250 = 15.8 m/s

Answer 2

http://www.wired.com/2010/09/maximum-range-in-projectile-motion/