# Solution of Relative Velocity Problem

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

cabin.

#### Solution Preview

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 ...

#### Solution Summary

A Solution of Relative Velocity Problem is provided. The magnitude and direction is found.