TARGET PRACTICE

Problem

A gun is positioned at ground level and a target is 1000 meters north of the gun and 100 meters above ground. A shell fired from the gun experiences a downward gravitational acceleration of 10 and an eastward Coriolis acceleration of 2 . Air resistance will be ignored. Set up the x,y,z axes with the gun at the origin, the x axis pointing East, the y axis pointing North, and the z axis pointing up.

1. If the initial velocity of the shell is then determine the position of the shell at time t in terms of a,b,c.
2. Find one choice of so that the shell hits the target - there are many choices for it.
3. What is the least speed with which the shell can be fired if it is to hit the target? Note that if initial velocity is then the initial speed is .
4. If there is a mountain range 400 meters high, running West to East, 400 meters north of the gun, then what is the least speed with which the shell may be fired if it is to reach the target?
5. Using Maple, plot the part of the trajectory of the shell in the cases (c) and (d) in the same picture. Also draw by hand the location of the mountain range and the target.

 
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