How Does a Tassel's Angle Reveal a Car's Acceleration?

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SUMMARY

The discussion focuses on calculating the acceleration of a car based on the angle of a tassel hanging from the rear-view mirror. When the tassel deflects backward at an angle of 5.60° from the vertical during acceleration, it indicates the presence of horizontal acceleration. The solution involves using trigonometric functions, specifically the tangent function, to relate the angle to the acceleration of the car. The key equation derived from the right triangle formed by the tassel's angle is a = g * tan(θ), where g is the acceleration due to gravity.

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Your friend's 10.9-g graduation tassel hangs on a string from his rear-view mirror. When he accelerates from a stop light, the tassel deflects backward toward the rear of the car. If the tassel hangs at an angle of 5.60° relative to the vertical, what is the acceleration of the car?


I realize this isn't difficult. I think I'm making it more complicated than it needs to be because I'm not sure how to start/ which equations to use. There's acceleration in both directions so I need to set up the x and y components of the acceleration/force but beyond that I'm lost. Any help with setting it up/ and or solving it would be much appreciated! I would rather you show the steps to solve it than the answer if at all possible. Thank you so much!
 
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Consider that acceleration is a vector too.

If the tassel is being pulled radially, then you have a right triangle where g is the vertical, and a of car is the horizontal.

Consider then tan-1 of the sides?
 

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