You are driving at a reasonable constant velocity in a van with a windshield tilted 120o 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.

Explanation:

The situation is represented in the free-body diagram attached to this answer.

We see that there are only two forces acting on the wallet:

- The force of gravity, downward, of magnitude , where m is the mass of the wallet and g is the acceleration due to gravity

- The normal reaction of the windshield on the wallet, N, in the direction perpendicular to the windshield

Resolving the normal reaction into the two directions - horizontal and vertical - the two equations of motion are:

Vertical:

Horizontal:

(2)

where

is the angle between the horizontal and the normal reaction

is the horizontal acceleration of the van

We can rewrite eq.(1) as

And dividing by eq(2),

And solving for a, we find the acceleration of the van:

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