a cannon is fired @ 50.0m/s @ 30.0deg.it lands @ the same height. What is Delta X?

Answer 1

vh (horizontal velocity) = 50 cos(30) = 50SQRT(3)/2 = 43.301 m/s
vv (vertical velocity) = 50 sin(30) = 25 m/s

First find the time to reach maximum height.
v = v0 + gt where g=9.8 m/s is the accelerations of gravity
v0 = vv = 25 m/s
v = 0 at maximum height
t = v0/g = 25/9.8 = 2.55102 seconds

Flight time is then twice this since the shell has to go up and then come back down.
T = 2*t = 2* 2.55102 = 5.102 seconds

DeltaX = (horizontal velocity)*(flight time)
DeltaX = 43.301*5.102 = 220.925 meters