posted by johnny .
A projectile is fired horizontally from a gun that is 97.0 m above flat ground, emerging from the gun with a speed of 250 m/s.
(a) How long does the projectile remain in the air?
(b) At what horizontal distance from the firing point does it strike the ground?
(c) What is the magnitude of the vertical component of its velocity as it strikes the ground?
Write equations of motion for the horizontal and vertical coordinates. Hasn't someone done that for you before?
(a) Solve the vertical motion equation for the time when the altitude is 0. The initial altitude is 97 m. The initial velocity will not matter in this case, since it is horizontal.
(b) X(final) = (initial velocity)*(time of flight)
(c) Add the change in potential energy to the initial kinetic energy, and get the final V from that.
Someone will be glad to critique your work. We will not do it for you.