Answer
The acceleration of the wallet is $~~(3.00~m/s^2)~\hat{i}+(6.00~m/s^2)~\hat{j}$
Work Step by Step
We can find an expression for the magnitude of acceleration of the purse:
$a_p = \frac{v_p^2}{r_p}$
$a_p = \frac{(\frac{2\pi~r_p}{T})^2}{r_p}$
$a_p = \frac{4\pi^2~r_p}{T^2}$
We can find an expression for the magnitude of acceleration of the wallet:
$a_w = \frac{v_w^2}{r_w}$
$a_w = \frac{(\frac{2\pi~r_w}{T})^2}{r_w}$
$a_w = \frac{4\pi^2~r_w}{T^2}$
We can find the ratio of $\frac{a_w}{a_p}$:
$\frac{a_w}{a_p} = \frac{\frac{4\pi^2~r_w}{T^2}}{\frac{4\pi^2~r_p}{T^2}} = \frac{r_w}{r_p} = \frac{3.00~m}{2.00~m} = 1.50$
Since the purse and the wallet are on the same radial line, the acceleration vector of both objects is in the same direction.
We can find the acceleration vector of the wallet:
$a_w = (1.50)(a_p)$
$a_w = (1.50)(2.00~m/s^2~\hat{i}+4.00~m/s^2~\hat{j})$
$a_w = (3.00~m/s^2)~\hat{i}+(6.00~m/s^2)~\hat{j}$
The acceleration of the wallet is $~~(3.00~m/s^2)~\hat{i}+(6.00~m/s^2)~\hat{j}$
