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