Velocity and Time Question?

Question

A river flows due east at 1.70 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.70 m/s due north relative to the water.
a. What is the velocity of the boat as viewed by an observer on shore?
b. If the river is 330 m wide, how far downstream has the boat moved by the time it reaches the north shore?

How do you solve this problem?

Answer 1

a. use pythagorean theorem on 1.70 and 9.70 to get the RESULTANT velocity which is the answer

b. time it reaches north shore....use the velocity NORTH and find the time v=d/t plug in the 330 and the 9. now plug in the time for v=d/t using the velocity east of 1.70 and the time you got

Answer 2

Nervous is quite right and I have voted for his answer. Here's another approach ( which turns out to be the same really).

1) Draw the picture (I drew mine with the river flowing across the page)
2) You can now see that the river flow does not affect the time taken to cross the water so do part b) first. Work out the time by dividing distance travelled north by speed travelling north. Now you can work out how far the boat difted downstream in that time.

3) draw the distance in on your picture to scale and work out the angle from a line drawn due north from where the boat set out to where it landed .

Answer 3

Part A:

This is a "triangle" problem. That is, there are two forces on the boat, and you're trying to find the sum of them. Luckily, since east is perpendicular to south, it's a right triangle and the answer looks something like this (Using pythagoras' theorom):

Velocity Observed is the square root of the sum of the Velocity East Squared and the Velocity South Squared.

VO = sqrt( VE^2 + VS^2 )

Draw a triangle like this:

......./ |
VO /..| VS
...../__|
......VE

Pythagoras tells us VO^2 = VS^2 + VE^2 for a right triangle.

VO^2 = 9.7*9.7 + 1.7*1.7
VO^2 = 96.98
VO= 9.85 m/s

Part B

330m / 9.7 m/s = how long it takes to cross = 34.02 seconds
1.7 m/s (drift speed) * 34.02 (how long it takes to cross) = 57.84 meters

Your boat will drift 57.84 meters downstream assuming you do nothing to correct course.