Answer
$162N\cdot s$
Work Step by Step
The required impulse can be determined as follows:
First, we apply the principle of impulse and momentum in the y-direction
$mv_{y_1}+\Sigma \int ^{t_2}_{t_1} F_y dt=mv_{y_2}$
We plug in the known values to obtain:
$0+Nt-6(9.81)t=0$
$\implies N=58.86N$
Now, we apply the principle of impulse and momentum in the x-direction
$mv_{x_1}+\Sigma \int ^{t_2}_{t_1}F_x dt=mv_{x_2}$
We plug in the known values to obtain:
$0+\int ^{t_2} _{t_1} F_x dt-(0.5)(9.81)(75)(0.4)=75(0.2)$
$\implies \int F_x dt=162N\cdot s$
