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Vectors: A hunter aims directly at a target; by how much will he miss the target?

A hunter aims directly at a target (on the same level) 103 m away. If the bullet leaves the gun at a speed of 255 m/s, by how much will it miss the target?

I'm assuming that the bullet will miss the target because it arcs down toward the ground as it moves horizontally. But don't I need to know how far off the ground it is in order to figure out how long it will take to hit the ground (and then use the time to determine how far it went)? If not, what do I do here?

Solution Preview

In horizontal direction the bullet has to travel 103 m with speed 255 m/s.
therefore, time taken by bullet to reach the vertical plane in which target is lying can be obtained as :
t = ...

Solution Summary

With formulas and good explanations, the problem is solved.