RelVel20
The are a few (3) types of question that you can expect in this section.
In this section we shall discuss the inteception of a moving body by another moving body
and considering the medium they move through to have no motion.
There are a couple of approaches to this question.
One is for two bodies to meet, the condition is to be at the same place at the same time, i.e. the coordinates are equal at the same time.
This is in effect was what Derek has presented.
Another is a vector approach. In this approach the relative velocity of the helicopter to the ship must be parallel to the position vector from the helicopter to the ship.
That means the helicopter flies directly to the ship.
2 boats a destroyer and a frigate pass each other in the ocean, at a certain time the destroyer is 250km east of the frigate, the frigate has a heading of 3i + 4j and the destroyer goes in the direction -7i + 1j
Calculate Vdf and Vfd, Do you see any similarities between the two results you just got ?
Remember that the
Vrelative = Vobject - Vobserver,
Draw what you know,,
what can you see that will help us to determine the shortest distance between the vessels as they move ?
solution
work out the relative velocity
draw a diagram that has the relative velocity vectors and the positions of each represented.
include the original distance.
the shortest distance shall be the perpendicular distance between the 'observer' and the line of the relative motion.
find the angle of the relative motion to the line of known distance, from the i & j vectors of the relavtive velocity, Tan ß = opp/adj.
if we now include the 90o angle we have 2 angles and a side and so we can determine all the sides ... thus we can determine the shortest distance between the vessels.
Other Questions include
How long did it take for them to reach this point (of shortest distance)?
How far has each car travelled by this stage?