(11 %) Problem 4: Assume that a woman flies 38 km in a direction 60° north of ea

Question

(11 %) Problem 4: Assume that a woman flies 38 km in a direction 60° north of east and then flies 25 km in a direction 15 north of east as shown in the figure 15° A+B R R ? Otheexpertta.com 50% Part (a) Find her distance R from the starting point in kilometers. Grade Summary Deductions 0% 100% sinO tanO Attempts remaining: 2 cotan asinacoso atan0 acotansinh0 coshO tan cotanhO ODegrees O Radians % per attempt) Hint Hints: deduction per hint. Hints remaining:4 Feedback: deduction per feedback 50% Part (b) Find the angle in ° N of E.

Explanation / Answer

Suppose given that Vector is V and it makes angle A with +x-axis, then it's components are given by:

Vx = V*cos A

Vy = V*sin A

Using above rule:

A = 38 km & angle = 60 deg N of E

Ax = A*cos A1 = 38*cos 60 deg

Ax = 19 km

Ay = A*sin A1 = 38*sin 60 deg

Ay = 32.91 km

B = 25 km & angle = 15 deg N of E

Bx = B*cos A2 = 25*cos 15 deg

Bx = 24.15 km

By = B*sin A2 = 25*sin 15 deg

By = 6.47 km

Now

R = A + B

R = (19 + 24.15) i + (32.91 + 6.47) j

R = 43.15 i + 39.38 j

Magnitude of R will be

|R| = sqrt (43.15^2 + 39.38^2) = 58.42 km

Direction = arctan (Ry/Rx)

= arctan (39.38/43.15) = 42.38 deg N of E

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