Explanation Given: The velocity of the plane υ A is 600 km/h . The velocity of the plane υ B is 500 km/h . The angle θ between the straight line is 75 ° . Relative velocity of plane B with respect to plane A is shown in Figure (1). From Figure (1) write the expression of relative vector velocity for plane A and plane B . v A = v B + v B / A (I). Write the expression for the magnitude of relative velocity υ B / A . υ B / A = υ x 2 + υ y 2 (II). Here, the magnitude of relative velocity is υ B / A and the velocity components is υ x and υ y Write the expression for the direction of components θ = tan − 1 υ y υ x (III). Here, the direction of the components is θ and the velocity components is υ x and υ y . Conclusion: From the Figure (1), Express v A in Cartesian form: v A = { 600 cos 75 ° i + 600 sin 75 ° j } km/h From the Figure (1), Express v B in Cartesian form v B = − { 500 i } km/h Substitute { 600 cos 75 ° i + 600 sin 75 ° j } km/h { − 500 j } km/h for v A and − { 500 i } km/h for v B in Equation (I)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 12.10, Problem 11RP

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The relative velocity of the plane B with respect to plane A :

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The relative velocity of the plane B with respect to plane A :

Solution Summary: The relative velocity of the plane with respect to plane A is shown in Figure (1).

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The relative velocity of the plane B with respect to plane A :

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