Answer
$P=205N$
Work Step by Step
We can determine the required magnitude of $P$ as follows:
We apply the principle of impulse and momentum in the y-direction:
$mv_{y_1}+\Sigma \int_{t_1}^{t_2} F_ydt=mv_{y_2}$
We plug in the known values to obtain:
$0+5+Psin30-(50)(90.81)(5)=0$
This simplifies to:
$N=490.5-0.5P~~~~$eq(1)
Now we apply the principle of impulse and momentum in the x-direction:
$mv_{x_1}+\Sigma \int_{t_1}^{t_2}F_xdt=mv_{x_2}$
We plug in the known values to obtain:
$0+(5)(0.2)N+5Pcos30=50(10)$
This simplifies to:
$4.33P-N=500~~~~$eq(2)
After solving eq(1) and eq(2), we obtain:
$N=387.97N$ and $P=205N$
