Explanation Figure 1 represents the motion of the whale in vector notation. Write the vector A → in unit vector notation. A → = A ( cos θ A i ^ + sin θ A j ^ ) (I) Here, A is the magnitude of vector A → , and θ A is the angle subtended by the vector A → with x axis. Given that the magnitude of vector A → is 360 km , and θ A makes an angle of 135 ° with the x axis. Apply the above condition in equation (I) and rearrange. A → = ( 360 km ) [ cos ( 135 ° ) i ^ + sin ( 135 ° ) j ^ ] = ( − 254.5 km ) i ^ + ( 254.5 km ) j ^ (II) Write the vector B → in unit vector notation. B → = B ( cos θ B i ^ + sin θ B j ^ ) Here, B is the magnitude of vector B → , and θ B is the angle subtended by the vector B → with x axis. Given that the magnitude of vector A → is 410 km , and θ B makes an angle of 90 ° with the x axis. Apply the above condition in equation (II). B → = 410 km [ cos ( 90 ° ) i ^ + sin ( 90 ° ) j ^ ] = 410 km j ^ (III) Write the resultant vector C → from Figure 1. C → = A → + B → (IV) Use equation (II) and (III) in equation (IV)

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ISBN: 9780135272992

Author: Wolfson

Publisher: VST

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Chapter 3, Problem 13E

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