Answer
(a) $P=54.88N$
(b) $W=1056J$
(c) $W=-1056J$
(d) $W=0$
Work Step by Step
(a) The shopping cart has a constant horizontal velocity, so there is no acceleration, and that means the horizontal forces balance each other.
If we call the pushing force $P$, its horizontal component will be $P\cos29^o$. Opposing this pushing force is friction $f$. We show above that these forces balance each other, so $$P\cos29=f=48N$$ $$P=\frac{48}{\cos29}=54.88N$$
(b) The component $P\cos29$ propels directly the movement of the cart for $s=22m$, so the work done is positive.
$$W=(P\cos29)s=48\times22=1056J$$
(c) Force $f$ has the same magnitude as $P\cos29$ and exerts force on the cart for the same $s=22m$, but since $f$ opposes the motion, its work is negative. $$W=-1056J$$
(d) Gravitational force points downward, so it does not influence the horizontal movement of the cart. Its work is $W=0$
