Question

Your projectile launching system is partially jammed. It can only launch objects with an initial vertical velocity of 42.0 m/s, though the horizontal component of the velocity can vary. You need your projectile to land 214 m from its launch point. What horizontal velocity do you need to program into the system?

Answer 1

the height is
h(t) = 42t - 4.9t^2 = t(42-4.9)
h=0 when t=8.57

so, after 8.57 seconds, the horizontal distance traveled is 214m. Since the horizontal component dies not change (much)

Vx = 214m/8.57s = 25 m/s

Answer 2

How did you come up with 4.9t^2?