04_P59InstructorSolution

04_P59InstructorSolution - Model Let the ground frame be S...

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4.59. Model: Let the ground frame be S and the car frame be S . S moves relative to S with a velocity V along the x -direction. Solve: The Galilean transformation of velocity is v v V = + G G G where and v v G G are the velocities of the raindrops in frames S and S . While driving north, ( ) ˆ 25 m/s V i = G and R R ˆ ˆ cos sin . v v j v i θ θ = − Thus, v v V ′ = G G G ( ) R R ˆ ˆ sin 25 m/s cos v i v j θ θ = − Since the observer in the car finds the raindrops making an angle of 38 ° with the vertical, we have R R sin 25 m/s tan38 cos v v θ θ + = ° While driving south, ( ) ˆ 25 m/s , V i = − G and R R ˆ ˆ cos sin . v v j v i θ θ = − G Thus, ( ) R R ˆ ˆ sin 25 m/s cos v v i v j θ θ ′ = − + G Since the observer in the car finds the raindrops falling vertically straight, we have
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