Question

A projectile is launched from and returns to ground level, as the figure shows. There is no air resistance. The horizontal range of the projectile is measured to be R= 166 m, and the horizontal component of the launch velocity is v0x = 26.0 m/s. Find the vertical component v0y of the projectile.

Answer 1

time in air = 166/26 = 6.38 s

so what stays up that long?
well, it spends half that time going up
t = 3.19 s upward

v = Vi - g t
at top v = 0
0 = Vi - 9.81(3.19)
Vi = 31.3 m/s initial speed up