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To test your FHE brother's claims about his car, you accept his offer of a ride about campus. Not wanting to exceed the speed limit, he claims he can only give a taste of the accelerating ability of his car and not the full proof. You notice, however, that the pine tree scented (and shaped) air freshener that hangs from his rear view mirror makes an angle of 26.0 degrees with the vertical while he is accelerating. What is the car's acceleration (m/s2 )?

Answer :

Manetho

Answer:

4.78 m/s^2

Explanation:

A)From he FBD

we can write

Tcosθ= mg

Tsinθ= ma

dividing we get tanθ= a/g

a= g tanθ

a= 9.81 tan26°= 4.78 m/s^2

The acceleration of the given car is [tex]4.78 \rm \ m/s^2[/tex]Acceleration can be defined as the rate of change in velocity.

What is acceleration?

Acceleration can be defined as the rate of change in velocity or direction of an object. The acceleration can be calculated by the formula,

[tex]a= g \rm \ tan\theta[/tex]

Where,

[tex]a[/tex] - acceleration

[tex]g[/tex] - gravitational force = 9.8 m/s²

[tex]\theta[/tex] - angle = 26°

Put the values in the formula,

[tex]a = 9.8 \times \rm \ tan 26 \\\\a = 4.78 \rm \ m/s^2[/tex]

Therefore, the acceleration of the given car is [tex]4.78 \rm \ m/s^2[/tex].

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