# Finding the acceleration given only an angle

This is one of my homework problems for a College Physics I course:

Dana has a sports medal suspended by a long ribbon from her rearview mirror. As she accelerates onto the highway, she notices that the medal is hanging at an angle of 12° from the vertical.

What is her acceleration (m/s2)? Express your answer using two significant figures.

What I don't understand is how I'm supposed to calculate anything given only that one angle, 12 degrees. Can someone help guide me to where to get started? Thanks.

• Remember that $\mathbf F$ is a vector, so draw a free-body diagram for the situation. – Kyle Kanos Sep 21 '14 at 19:29

Draw a diagram, then you'll find out the answer. If $\mathbf T$ is the tension in the string, $\delta$ is the angle, $m$ is the mass of the medal and $\mathbf g$ is the gravitational acceleration then $$T\cos\delta=mg$$ and $$T\sin\delta=ma$$ where $a$ is the acceleration, then $$\tan\delta=\frac{a}{g}$$ $T, m,\cos\delta\neq 0$ which leads $$a=g\tan\delta$$
If $T$ is equal to $0$ then the mass of the medal would be $0$, the same would happen if $\cos\delta=0$. Now, if $\sin\delta=0$ then there would not be acceleration at all ($m$ cannot be zero).