A boat pushes off from a pontoon and travels 5m/s East while the pontoon floats away at 2m/s south. Calculate the velocity of the boat relative to the pontoon????? .
1 Answer
If you don't understand the vector concept, go to Method B.
Method A: vector method.
Let
Relative velocity means comparing
The magnitude of
The direction of
Method a) Reasoning without using vector concept
Method B: reasoning without using vectors.
Let
x = distance traveled by the boat t seconds due E after the pushing
y = distance traveled by pontoon t seconds due S after the pushing
At t=1.0 s later,
x= 5 m East
y = 2m South.
x and y form an right angle triangle.
Then distance (d) between them (from center of mass of the boat to the center of mass to the pontoon if you want) is
The rate of this separation is therefore
Hence the boat is moving away relative to the pontoon at a speed 5.4 m/s.
To find which direction the boat is moving away relative to the pontoon, you have to imagine that you are sitting on the pontoon facing south. To see which direction the boat is moving away, you have to turn your head to the east, then northward. Hence the boat is traveling in the NE direction.
The angle, illustrated in the figure above, is thus:
(Note, the answer can be simply written as
Finally,
the velocity of the boat relative to the pontoon:
It has a speed 5.4 m/s and at an angle