At 1:00 pm a ship A leaves port P. It sails in the direction 030 at 12 km h1. At the same time, ship B is 100 km due east of P, and is sailing at 8 km h1 towards P. a Show that the distance D(t) between the two ships is given by D(t) = p 304t2 2800t + 10 000 km, where t is the number of hours after 1:00 pm. b Find the minimum value of [D(t)]2 for all t > 0. c At what time, to the nearest minute, are the ships closest?
Conference 1 – MA 1022 WPI C 2017 Johnson Finish what you can (and let me know how far you went). I don’t expect you to go through everything. Use this as a reference for them if needed. 1 I did not have a chance to cover these problems in class. Do your best to tease out work and answers. Solve the initial value problem: ds= 6 sin(3 ) 1cos(2 ); sπ = 3 dt 3 6 2 • Challenge: Remind them of Integration s (t) = Position Start with a(t) s ‘ (t) = v(t) v ‘ (t) = a(t) They will need a lot of help with this – see how well they relate to initial conditions (can they come up with them) and understand what to solve for. 3 • Rectangles to estimate area. i) Calculate left and right endpoint areas with 4 rectangles. Just do the basics of the calculation ( ∆x =1 ) and the appropriate function values and sum. ii) Midpoint (Riemann) with 4 rectangles. 4 Conference 2 – MA 1022 WPI C 2017 Johnson 35 minutes of problem work Problem 1 Section 5.2 Problem 2 Infinite Riemann sum for 3 f (x)= 2x −4x; x:[−2, 0] 1 Problem 3 Evaluate by using definite integral: 5 ∫ − x 2+ 7 x− 10) dx 2 Problem 4 Evaluate (by use of area) (Not likely to
