Shooting Over A Mountain

Physlet Assistance
on      off
vm/s q   Position of Boat = 
 
Your artillery battalion is stationed on the inland side of a mountain range.  Your commander orders you to fire on ships that pass by just off-shore.  In order to conserve munitions, you know that you should calculate the minimum and maximum angles that the projectile can have in order to make it over the mountains. You control both the angle and speed (5 m/s < v < 100 m/s) of the projectiles. What range of distances off-shore can you hit?  Are there any places where ships are safe to travel?

Hints

  1. For a given speed, what minimum angle must the projectile have in order to make it over the mountain?  
  2. Is there a maximum angle?  Why?
  3. What is the range of a projectile fired at a particular velocity?

Reference

See  Serway and Beichner, Physics For Scientists and Engineers 5th Edition, Problem 4.70


Illustration written by Chuck Niederriter