Answer:
[tex]17.0 m/s^2[/tex]
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 [tex]mg[/tex], 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:
[tex]N sin \theta - mg =0[/tex]
Horizontal:
[tex]N cos \theta = ma[/tex] (2)
where
[tex]\theta=30^{\circ}[/tex] is the angle between the horizontal and the normal reaction
[tex]a[/tex] is the horizontal acceleration of the van
We can rewrite eq.(1) as
[tex]N sin \theta = mg[/tex]
And dividing by eq(2),
[tex]tan \theta = \frac{g}{a}[/tex]
And solving for a, we find the acceleration of the van:
[tex]a=\frac{g}{tan \theta}=\frac{9.8}{tan 30^{\circ}}=17.0 m/s^2[/tex]
