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Question

Need help with this problem. Someone please explain. Thanks a lot!

You have a boat with a motor that propels it at vboat = 4.5 m/s relative to the water. You point it directly across the river and find that when you reach the other side, you have traveled a total distance of 27 m and wound up 14 m downstream. What is the speed of the current?

Answer 1

if you are going 4.5m/s then you have traveled in two directions, straight across and downstream. If you make a drawing of this it will create a triangle with 2 sides of the river and a hypotenuse of the distance traveled, 27.
you know one side on the river is 14, the hypotenuse is 27
the pythagorean theorem says that A squared + B squared = C squared for a right sided triangle
so 14 squared + distance across river squared = 27 squared
D squared = 729 - 196
d = square root of 533
d= 23.08
so the distance traveled at 4.5m/s was 23.08
we know that d = r * t
so t = 23.08/4.5

t = 5.15 s

we also know that in 5.15s the boat went 14 m downstream
againg d=rt
14 = r * 5.15
r (speed of current) = 14/5.15
r= 2.71m/s

Answer 2

you need to use pythagoras to find the width od the river from the 27m (diagonal) and the 14m

(i make it 23m)

that will tell you how long it took you to cross the river in seconds from the speed of the boat and the width of the river.

( i reckon 5.13 s)

the speed of the river can be used from that 14m downstream and the total time you were travelling

(i think 2.7 m/s)

check my numbers, i',m very drunk right now

Answer 3

One heck of a lot. Close to the speed of the boat.