Alice and Bob use the mechanism shown in the following figure for authentication. In specific, after Alice informs Bob she wants to communicate, Bob generates a random number R and sends it back to Alice.

Assume R fits into a single block and Alice encrypts R in CBC mode, so $\{$R$\}$KAB is computed as $\{$IV xor R$\}$KAB$,$ where IV is Alice created for CBC operation. Alice then sends IV and $\{$IV xor R$\}$KAB to Bob, as shown in the $3$rd message in the figure.

Suppose Eve sees an exchange between Alice and Bob, where the challenge is R$1.$ How can Eve then impersonate Alice, during a different conversation where Bob sends a different challenge R$2?$

To get full credit, completely describe the content of messages Eve sends to Bob, and at what time. That is$,$ you need to describe the message exchange in a timeline.

Please explain it cleary and in details because I am learning about it$.$