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.

Question

Physics

Nemo

29 December, 10:59

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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Fernanda Church · Answer 1

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