Answer
$(a)\space 5.5\space km$
$(b)\space 9.1\space km$
Work Step by Step
Please see the attached image first.
Let's take,
Displacement vector of blue boat $=S_{B}$
Displacement vector of green boat $=S_{G}$
West, south components of displacement vector of blue boat $=S_{BW},S_{BS}$
West, south components of displacement vector of green boat $=S_{GW},S_{GS}$
Because both boats travel at 101 km per hour, each one ends up $(0.5\space h)(101\space km/h)=50.5\space km$ from the dock after a half-hour. So,
$|S_{B}|=|S_{G}|=50.5\space km$
We can write,
$S_{BW}=S_{B}cos25^{\circ}=(50.5\space km)(0.9)=45.8\space km$
$S_{GW}=S_{G}sin53^{\circ}=(50.5\space km)(0.8)=40.3\space km$
The blue boat travels further than the green boat by,
45.8 km - 40.3 km = 5.5 km
(b) Similarly,
$S_{BS}=S_{B}sin25^{\circ}=(50.5\space km)(0.4)=21.3\space km$
$S_{GS}=S_{G}cos53^{\circ}=(50.5\space km)(0.6)=30.4\space km$
The green boat travels further than the blue boat by,
30.4 km - 21.3 km = 9.1 km
