Answer
The ratio of the refrigerator’s speed in case 2 to its speed in case 1 is $~~cos~\theta$
Work Step by Step
Case 1: We can find the acceleration:
$F = ma_1$
$a_1 = \frac{F}{m}$
We can find the speed at time $t$:
$v_1 = a_1~t = \frac{F~t}{m}$
Case 2: We can find the acceleration:
$F~cos~\theta = ma_2$
$a_2 = \frac{F~cos~\theta}{m}$
We can find the speed at time $t$:
$v_2 = a_2~t = \frac{F~cos~\theta~t}{m}$
We can find the ratio of $\frac{v_2}{v_1}$:
$\frac{v_2}{v_1} = \frac{\frac{F~cos~\theta~t}{m}}{\frac{F~t}{m}}$
$\frac{v_2}{v_1} = cos~\theta$
The ratio of the refrigerator’s speed in case 2 to its speed in case 1 is $~~cos~\theta$
