FOLLOWING PROBLEM

For this problem, we will try to model the path of a missile pursuing a target. The target's path is given,

Ti(t) = (xt (t), yt (t), zt (t)), and the missile starts at the origin, 7(0) = (0,0,0)

You must model the motion of the missile under three conditions.

a) The missile always moves at a given top speed Vmax directly towards the target.

b) The missile accelerates at a fixed rate amax directly towards the target

For both cases, plot the trajectory of the missile and target in a figure window (using plot3), and also

build a separate plot of the distance between the two vs. time.

Case a) performs better than case b), but it's not clear whether such a solution is possible. To examine

this, I want you to calculate the acceleration of the missile for case a). To do this, you must numerically

differentiate each velocity component (0 (At2) is fine) and take the magnitude of the resulting vector.

That is, a(t) = || (x(t)), (y(t)), (z(t)))||. Reminder, our numerical differentiation methods

require an evenly spaced t vector.

Plot the acceleration vs. time for case a)

TARGET

For the target above, any reasonable target path is fine, so long as the problem is actually 3D, and the

missile can actually catch the target. An example trajectory might be

$(36) ₁/²+ +0.12t, sin

1000 (1 + cos