You are driving at a reasonable constant velocity in a van with a windshield tilted 120​o​ relative to the horizontal. As you pass under a u

Question

You are driving at a reasonable constant velocity in a van with a windshield tilted 120​o​ relative to the horizontal. As you pass under a utility worker fixing a power line, the worker’s wallet falls onto the windshield. Determine the acceleration needed by the van so that the wallet stays in place if frictional forces are negligible.

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RI SƠ 2 months 2021-07-30T01:23:50+00:00 1 Answers 4 views 0

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    2021-07-30T01:25:08+00:00

    The vectors are broken into components in orthogonal directions.The orthogonal vector components are treated independently of each other.

    The acceleration of van is a= 11 m/s ²

    Explanation:

    We can solve this problem based on its accelerations , The acceleration due to gravity will have two components relative to the windshield, parallel and perpendicular, given by

    g║= g sin θ

    g⊥ = g cosθ

    The acceleration due to van will also have same two components , but the acceleration is along the horizontal, than vertical the trig functions will be opposite what they were for gravity.

    a║= a cos θ

    a⊥= a sin θ

    To isolate the van’s acceleration

     a= g sin (θ) ± μs cos (θ) / cos (θ) ± μs sin (θ)

    θ = 180°- 120°

       = 60°

    We can assume that van is not decelerating with 30 g’s and giving the acceleration of the van as

      a= 11 m/s²

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