In this problem, a life boat slides halfway to the water, gets stuck for a moment, then starts up again. The lifeboat moves along a ramp angled $theta = 60^{circ}$ relative to the vertical. It has mass $m = 4900~mathrm{kg}$ and the magnitude of the displacement is $d = 5.0~mathrm{m}$. We use $g = 9.81~mathrm{m/s^{2}}$.

The force is the weight of the lifeboat. The angle between the force does not change, and the total displacement is unchanged. The work done by gravity is

$$
begin{align*}
W &= vec{mathbf{F}} cdot vec{mathbf{d}} \
&= mvec{mathbf{g}} cdot vec{mathbf{d}} \
&= mgd cos theta \
&= left( 4900~mathrm{kg} right) left( 9.81~mathrm{m/s^{2}} right) left( 5.0~mathrm{m} right) cos 60^{circ} \
&= 120172.5~mathrm{J} \
W &= boxed{ 120000~mathrm{J} }
end{align*}
$$

$$
W = 120000~mathrm{J}
$$

In this problem, a parent pulls a child in a little red wagon. The parent exerts a force of $F = 16~mathrm{N}$ over a distance of $d = 12~mathrm{m}$ and the handle of the wagon is at an angle of $theta = 25^{circ}$ above the horizontal. We calculate the work done by the parent.

The angle between the displacement and the force is $theta$. We have

$$
begin{align*}
W &= vec{mathbf{F}} cdot vec{mathbf{d}} \
&= Fd cos theta \
&= left( 16~mathrm{N} right) left( 12~mathrm{m} right) cos 25^{circ} \
&= 174.01110~mathrm{J} \
W &= boxed{ 174~mathrm{J} }
end{align*}
$$

$$
W = 174~mathrm{J}
$$