Answer
$I = 5.0~A$
The current flows clockwise around the loop.
Work Step by Step
We can find the induced voltage in the loop:
$\Delta V = B~v~L$
$\Delta V = (0.20~T)(50~m/s)(0.050~m)$
$\Delta V = 0.50~V$
We can find the induced current:
$I = \frac{\Delta V}{R}$
$I = \frac{0.50 ~V}{0.10~\Omega}$
$I = 5.0~A$
As the loop goes up, there is more magnetic flux going through the loop directed out of the page. By Lenz's law, a current is induced around the loop which opposes the change in flux. Then, the current must produce a magnetic flux directed into the page. By the right hand rule, this current flows clockwise around the loop.
