Explanation Given: The relative velocity of car B with respect to car A is shown in Figure (1). The radius of curvature is ρ is 0.5 mi . The increasing velocity ( a B ) t is 1200 mi/h 2 . The velocity of the car υ A is 55 mi/h . The velocity of the car υ B is 40 mi/h . The car A maintains the constant velocity a A =0. From Figure (1) write the expression of relative velocity for car A and car B . v B / A = v B − v 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 . From Figure (1) write the expression of relative acceleration for car A and car B . a B / A = a B − a A (IV). Write the expression for the magnitude of relative acceleration a B / A . a B / A = a x 2 + a y 2 (V). Here, the magnitude of relative acceleration is a B / A and the acceleration components is a x and a y Write the expression for the normal acceleration ( a B ) n . ( a B ) n = υ B 2 ρ (VI). Here, normal acceleration is ( a B ) n , velocity of the car B is υ B and radius of curvature is ρ . Write the expression for the direction of components θ = tan − 1 a y a x (VII). Here, the direction of the components is θ and the acceleration components is a x and a y Conclusion: From the Figure (1) Express v A in Cartesian form v A = { − 55 i } mi/h From the Figure (1) Express v B in Cartesian form v B = { − 40 cos 30 ° i + 40 sin 30 ° j } = { − 34.64 i + 20 j } mi/h Substitute { − 55 i } mi/h for v A and { − 34.64 i + 20 j } mi/h for v B in Equation (I). v B / A = v B − v A v B / A = { − 34.64 i + 20 j } mi/h − { − 55 i } mi/h v B / A = { 20

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Author: HIBBELER

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Chapter 12, Problem 219P

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The velocity and acceleration of the car B with respect to car A and direction angle of components.

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Chapter 12, Problem 218P

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The velocity and acceleration of the car B with respect to car A and direction angle of components.

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The velocity and acceleration of the car B with respect to car A and direction angle of components.

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