Answer:
The acceleration of the wallet is [tex]3\hat{i}+6\hat{j}[/tex]
Explanation:
Given that,
Radius of purse r= 2.30 m
Radius of wallet r'= 3.45 m
Acceleration of the purse [tex]a=2\hat{i}+4.00\hat{j}[/tex]
We need to calculate the acceleration of the wallet
Using formula of acceleration
[tex]a=r\omega^2[/tex]
Both the purse and wallet have same angular velocity
[tex]\omega=\omega'[/tex]
[tex]\sqrt{\dfrac{a}{r}}=\sqrt{\dfrac{a'}{r'}}[/tex]
[tex]\dfrac{a}{r}=\dfrac{a'}{r'}[/tex]
[tex]\dfrac{a'}{a}=\dfrac{r'}{r}[/tex]
[tex]\dfrac{a'}{a}=\dfrac{3.45}{2.30}[/tex]
[tex]\dfrac{a'}{a}=\dfrac{3}{2}[/tex]
[tex]a'=\dfrac{3}{2}\times(2\hat{i}+4.00\hat{j})[/tex]
[tex]a'=3\hat{i}+6\hat{j}[/tex]
Hence, The acceleration of the wallet is [tex]3\hat{i}+6\hat{j}[/tex]
