In: Physics
Suppose that a cannon tower of 1000 feet height was erected at the origin of the coordinate space. The speed of the cannonballs launched by the tower is 1000 feet per second. An armored vehicle is patrolling in a circular path around the tower 8000 feet away at a speed of 10 feet per second. Coordinates was chosen such that at time zero the location of the vehicle is (8000, 0, 0).
(a) Describe the motion of the vehicle with a vector valued function with respect to time t.
(b) At time zero, a cannonball is launched from the tower in the direction of u = <u1,u2,u3>, where ||u|| = 1. Ignoring all resistive forces, describe the motion of the cannonball with a vector valued function with respect to time t. Gravitational acceleration g = 32 ft/s2.
(c) Determine whether it is possible for the cannonball to hit the vehicle. If it is, find the direction in which the cannonball should be launched, and express your answer as a unit vector.