(a) Explanation Given Information: The relative velocity ( v A / w ) of the airplane with respective to wind is 300 mi/h at an angle ( θ ) of 30 ° (north to east). The relative velocity ( v A / B ) of the airplane with respective to ship is 280 mi/h at an angle ( ϕ ) of 33 ° (north to east). The ship is steaming due south at the speed ( v B ) of 12 mi/h . Calculation: Write the relative velocity ( v A / w ) of the airplane with respective to wind in terms of vector notation. v A / w = v A / w ( sin θ i + cos θ j ) Substitute 300 mi/h for v A / w , and 30 ° for θ . v A / w = 300 ( cos 30 ° i + sin 30 ° j ) = 259.81 i + 150 j Write the relative velocity ( v A / B ) of the airplane with respective to ship in terms of vector notation. v A / B = v A / B ( sin θ i + cos θ j ) Substitute 280 mi/h for v A / B , and 33 ° for θ . v A / B = 280 ( cos 33 ° i + sin 33 ° j ) = 234.828 i + 152.499 j Write the speed of ship ( v B ) in vector notation: v B = − 12 j Calculate velocity vector ( v A ) of the airplane using the relation below: v A = v B + v A / B Substitute − 12 j for v B and 234 (b) To determine The wind speed ( v A ) and direction ( α ) .

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 11.4, Problem 11.130P

(a)

To determine

The velocity (vA) of the airplane.

(b)

To determine

The wind speed (vA) and direction (α).

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Chapter 11.4, Problem 11.129P

Chapter 11.4, Problem 11.131P

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The velocity ( v A ) of the airplane.

Solution Summary: The author calculates the relative velocity (v_A/w) of the airplane with respective to wind in terms of vector notation.