Optimal control problems II Exercise 1 Solve first for a = 0, then for a = 1 s.t. min J(u) = L(2x (2x-3u - 1 - 오리(t)2) dt บ dx = x+u dt Exercise 2 x(0) = 5, 0 ≤u ≤ 2 s.t xkx+bu, 1 min J(u) = ²() de (0.1) x(0)=xo, x(T) = xT (specified). (0.2)

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.