Answer
(a) The displacement vector is $(1.73~\hat{i}-3.0~\hat{j})~cm$
(b) The displacement is zero.
Work Step by Step
(a) At 8:00, the minute hand points straight up. At 8:20, the minute hand makes a $30^{\circ}$ angle below the positive x-axis. We can find the x-component and the y-component of the displacement as:
$\Delta x = (2.0~cm)~cos(30^{\circ})$
$\Delta x = 1.73~cm$
$\Delta y = -(2.0~cm)~sin(30^{\circ})-(2.0~cm)$
$\Delta y = -3.0~cm$
The displacement vector is $(1.73~\hat{i}-3.0~\hat{j})~cm$
(b) At 8:00 and 9:00, the minute hand points straight up, so the displacement is zero.
