Answer
$I=5.68N\cdot s$
Work Step by Step
We can determine the magnitude of the required net impulse as follows:
According to the impulse momentum principle in the vertical direction
$mv_1+I_y=mv_2$
We plug in the known values to obtain:
$0.2\times 0+I_y=(0.2\times 20sin40)$
This simplifies to:
$I_y=2.5711N$
Now we apply the impulse momentum principle in the horizontal direction
$mv_1+I_x=mv_2$
We plug in the known values to obtain:
$0.2\times (-10)+I_x=0.2\times 20cos40$
$\implies I_x=5.06417N\cdot s$
Now $I=\sqrt{I_x^2+I_y^2}$
We plug in the known values to obtian:
$I=\sqrt{(2.5711)^2+(5.06417)^2}$
$\implies I=5.68N\cdot s$
