You are Sitting in a small boat holding the end of a rope.The other end of the rope is tied to the top of
a nearby pier (See figure) , such that the it is higher above the water than your end of the rope,Causing your boat to move towards the pier,stopping directly underneath the pier.As you pull on the rope, which is moving faster :boat or the rope?
i.e the speed of the boat moves across the water or the speed the rope moves through your hands.
Looks like difficult one but not exactly.
Boat faster:) boat travels greater distance than rope in the same period..
ReplyDeleteWe can go about this using simple calculus :D.
ReplyDeleteOr we can observe the limiting case:
H -> Height of the pulley.
D -> Distance of the boat.
R -> Length of the rope.
Now at any given point:
R< H+D(Triangular inequality).
Consider the limiting case where D->0
Now R will equal H.
Now from a point R <H+D we have moved to R = H. So the decrease is <D. Hence proved!
Thanq buddies :-)
ReplyDelete