(17%) Problem 3: west of north Suppose you walk 12.5 m in a direction exactly 23
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(17%) Problem 3: west of north Suppose you walk 12.5 m in a direction exactly 23° south of west then you walk 18 m in a direction exactly 45 25% Part (a) How far are you from your starting point in m? Grade Summary Deductions Potential 0% 100% tan0 t acos0 sinh0 cosh0 n cotanh0 Submissions Attempts remaining: Z (3% per attempt) detailed view ( sin cotan0 asin) atan)acotan) cosO 0 Degrees O Radians CLEAR 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 18 m in a direction exactly 45° west of north, and then leg A, which is 12.5 in a direction exactly 23° 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:?Explanation / Answer
Lets resolve the vector A into components
angle from positive x axis, = 180 + 23 = 203 degree
Ax = A * cos
= 12.5 * cos(203.0)
= -11.5063
Ay = A * sin
= 12.5 * sin(203.0)
= -4.8841
Lets resolve the vector B into components
angle from positive x axis, = 90 + 45 = 135 degree
Bx = B * cos
= 18.0 * cos(135.0)
= -12.7279
By = B * sin
= 18.0 * sin(135.0)
= 12.7279
we have:
A = -11.5063i- 4.8841j
B = -12.7279i+ 12.7279j
R = A + B
R = (-11.5063i- 4.8841j) + (-12.7279i+ 12.7279j)
= (Ax + Bx)i + (Ay + By)j
= (-11.5063 - 12.7279)i + (-4.8841 + 12.7279)j
= -24.2342i+ 7.8438j
a)
magnitude of R = sqrt (-24.2342^2 + 7.8438^2)
magnitude of R = 25.472
Answer: 25.5 m
b)
Since x component is negative and y component is positive
It lies in the 2nd cordinate
angle = 90 + atan(|x/y|)
angle = 90 + atan(|-24.2342/7.8438|)
angle = 162 degree from x axis
which is north of west = 180 - 162 = 18 degree
Answer: 18 degree
c)
It will not make any difference as displacement is still same
Answer: 25.5 m
d)
Answer: 18 degree
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