Answer
$P=224~N$
Work Step by Step
We can determine the magnitude of the required force $P$ as follows:
As $v=v_{\circ} +at$
$\implies 4=0+at$eq(1)
and $s=s_{\circ}+v_{\circ}t+\frac{1}{2}at^2$
$\implies 5=0+0+\frac{1}{2}at^2$
$at^2=10$.eq(2)
Solving eq(1) and eq(2), we obtain:
$t=2.5s$ and $a=1.6m/s^2$
Now we apply Newton's second law
$\Sigma F_y=0$
$\implies N-W+Psin\theta=0$
$\implies N=W-Psin\theta$
We plug in the known values to obtain:
$N=(50)(9.81)-Psin30=490.5-0.5P$
and $\Sigma F_x=ma_x$
$\implies -\mu_k N+Pcos\theta=ma$
We plug in the known values to obtain:
$-0.3(490.5-0.5)+Pcos30=(50)(1.6)$
This simplifies to:
$P=223.567N\approx224~N$
