A leaf is blown by the wind. The leaf moves five metres forward
and then three metres backward. What is the distance moved by the
leaf? What is the leaf’s net forward
Okay, so in this question, we’ve
got a leaf. And that leave is blown by the wind
so that it moves five metres forward and then it moves three metres backward. So the leaf starts out in this
position here and it ends up in this position here. What we’ve been asked to do is to
firstly find the distance moved by the leaf.
Well, we can recall that distance
is defined as the length of a path between two positions. In this case, the two positions are
the start position and the end position of the leaf. And so, the path taken by the leaf
is to firstly go five metres forward and then come back three metres. And hence, the total distance that
the leaf has travelled — let’s call that distance 𝑑 — is equal to the five metres
forward plus the three metres it travelled back.
Because even though the leaf came
back and travelled in the opposite direction to its initial motion, that doesn’t
matter when we try to calculate distance. All that matters is the total path
length. And this total path length is five
metres plus three metres which ends up being eight metres. Therefore, we can say that the
distance moved by the leaf is eight metres.
Now the second part of the question
asks us to find the leaf’s net forward displacement. Now, net simply means overall or
resultant. And so, we’re just trying to find
the overall forward displacement of the leaf. Now, displacement is defined as the
straight line distance or in other words the shortest distance between two
positions, in this case between the starting position and the ending position once
Well, in this situation, the
straight line distance between those two points is this distance here. But then, that distance is equal to
this whole five metres minus this three-metre distance here. And so, we can say that the
displacement of the leaf which we will call 𝑠 is equal to five metres — that’s the
whole distance it moves forward — minus the three metres that it moves back. And five metres minus three metres
is equal to two metres.
Now there’s a couple of things we
haven’t considered here. Firstly, we need to recall that
displacement is a vector quantity. So this means that it has magnitude
or size and direction. So why have we not stated direction
here when we’ve worked out the displacement of the leaf? Well, it’s because we don’t need
to; the question has done it for us. We’ve been asked to find the least
net forward displacement.
And in fact, overall, the leaf does
move forward because the net effect the overall effect of moving five metres forward
and then three metres back is equivalent to the leaf just having moved two metres
forward. And so, what we’ve done is
calculated the forward displacement of the leaf. And it would be unnecessary to
write two metres forward when we’ve been asked to find the forward displacement.
So in a situation like this, we
don’t need to write the direction. But in general, we should. It’s a good idea to write the
direction. But anyway, so we found our final
answer. Now the leaf’s net forward
displacement is two metres.