Class Management Help Vectors Begin Date: 2/27/2017 12:00:00 AM Due Date: 6/28/2
ID: 1629169 • Letter: C
Question
Class Management Help Vectors Begin Date: 2/27/2017 12:00:00 AM Due Date: 6/28/2017 11:00:00 PM End Date: 8/2/2017 11:00:00 PM (8%) Problem 6: Suppose you walk 11 m in a direction exactly 239 south of west then you walk 19 m in a direction exactly 35 west of north. 25% Part (a) How far are you from your starting point in m? Grade Summary Deductions Potential 1% 99% sinO cosO cotan0 asin acos0 atanO acotan sinh0 cosh0 tan cotanh0 Submissions Attempts remaining: 19 (100 per attempt) detailed view END 196 Degrees Radians NO Submit Hint I give up! Hints: 0% deduction per hint. Hints remaining: 3 Feedback: 1% deduction per feedback 25% Part (b) What is the angle of the compass direction of a line connecting your starting point to your final position measured North of West in degrees? 25% Part (c) Repeat part (a) by finding your distance from the starting point in m. but reverse the order of the two legs of the walk. That is. you first walk leg B, which is 19 m in a direction exactly 35° west of north, and then leg A, which is 11 in a direction exactly 22° south of west - ) 25% Part (d) What is the angle of the compass direction of a line connecting your starting point to your final position measured North of West in degrees? All content& 2017 Expat TA, LLCExplanation / Answer
(a) Consider East-North cartesian system
First displacement vector, d1 = 11(-cos22oE - sin22oN)
Second displacement vector, d2 = 19(-sin35oE + cos35oN)
Net displacement vector, d = d1 + d2
=> d = 11(-cos22oE - sin22oN) + 19(-sin35oE + cos35oN)
=> d = -(11cos22o + 19sin35o)E + (19cos35o - 11sin22o)N
=> d = -21.10E + 11.44N
Distance from origin, R = [(-21.10)2 + 11.442]1/2 = 24 m
(b) Direction, = tan-1(11.44 / 21.10) = 28.5o (North of West)
(c) Even if you reverse the order, we can see that the net displacement vector will be the same since the net displacement is simply the sum of two displacements. This means that the final position in this case remains the same as in previous case, Hence, the distance from origin is same i.e. 24 m
(d) Same final position means the angle of compass direction will be the same i.e. 28.5o