Relative Velocity Problem
Consider a boat on the West bank of a river of width D=1664 meters to be at the origin of an x,y axis system with the 0° direction East along the +x axis.
The river water runs South with velocity vector W= 3.9 m/sec at 270°.
At coordinates (1200, -390) is a dock on an island. At coordinates (1664, 0) is a cabin. The boat starts at (0,0), pointing to a heading of 0°, with unknown speed B relative to the water. Combined with the current velocity, it moves in a straight line to the dock with actual velocity A, arriving in 100 seconds.
Carefully observe the problem attachment, a picture illustrating all given
information in Fig. 1.
a. Find the magnitude and direction of
actual velocity vector A.
b. Construct a polygon connecting vectors
W, B, and A. Solve this vector
triangle, Fig. 2, to find B, the speed of
the boat relative to the water.
c. With B, the boat's speed relative to the
water, known from part b, the
boat now heads in a direction such that
it travels in a straight line to the
cabin with velocity over ground vector V.
Find the required heading of the boat
and the time to move from dock to
Solution of Relative Velocity Problem
a. The distance from origin to dock is;
D=sqrt(1200^2+390^2)= 1262 m
which the boat travels in 100 seconds.
Therefore, the speed of the boat, (the
magnitude of vector A), is:
A=D/t= 1262 m/100 sec = 12.62 m/sec.
The line from origin to dock is at angle
p° = invtan (-390/1200) = -18° and ...
A Solution of Relative Velocity Problem is provided.