A Projectile Is Fired

Problem: A howitzer fires a projectile at 220 m/s at an angle of 34^o. The howitzer is emplaced on the side of a hill 150 m above a level plain.

a) How high does the projectile go above the plain?

b) How far down range will it go?

c) How much time will it take?

Solution: a) Since the y-velocity is zero at the projectile's highest point,

This is the time required to reach the highest point. (Incidentally, it cannot be doubled to find the total time since the starting point is not at the same elevation as the target point.) I now use the equation for displacement in the y-direction:

Since I have taken the firing point as the origin, I have to add 150 m to this, getting 922 m above the plain.

b and c) When the projectile hits the target, the displacement in the y-direction will be -150 m:

The negative time is non-physical and is discarded. Substituting the 26.3 seconds in for t in the equation for x, I get 4792 m. To three digit accuracy, this is 4.79 km.