Ferry Captain: Finding Direction & Resultant Velocity

[pivoxa15]

Homework Statement

A ferry captain wishes to travel directly across a river. A current of 4km/h is flowing and the ferry can travel at 8km/h.
a) In what direction should the captain direct the ferry?
b) What is the resultant velocity of the ferry as seen by someone standing on the riverbank?

Homework Equations

The Attempt at a Solution

a) The ferry should be directed to travel 26.6 degrees up stream so that it will travel in a straight line. - same as the answers.

b) I don’t get. It’s not sqrt(8^2+4^2) because it travels in a straight line now. Would it simply be 8km/h? The answers suggested 6.9m/s.

 

[denverdoc]

Homework Statement

A ferry captain wishes to travel directly across a river. A current of 4km/h is flowing and the ferry can travel at 8km/h.
a) In what direction should the captain direct the ferry?
b) What is the resultant velocity of the ferry as seen by someone standing on the riverbank?

Homework Equations

The Attempt at a Solution

a) The ferry should be directed to travel 26.6 degrees up stream so that it will travel in a straight line. - same as the answers.

b) I don’t get. It’s not sqrt(8^2+4^2) because it travels in a straight line now. Would it simply be 8km/h? The answers suggested 6.9m/s.

to the viewer on the river bank it comes directly at it, so the apparent distance traveled is 8km. But the actual speed toward the river bank is reduced by the angle upstream. I would think that angle would be 30, and
cos(30)*8=6.9km/hr

 

[pivoxa15]

to the viewer on the river bank it comes directly at it, so the apparent distance traveled is 8km. But the actual speed toward the river bank is reduced by the angle upstream. I would think that angle would be 30, and
cos(30)*8=6.9km/hr

I still don't see how you arrived at this answer. Maybe could yo draw a diagram?

 

[denverdoc]

To overcome the current, is the direction of the ferry, having X ,----I
a component of 4Km/hr upstream to offset the drift. Since...X----I
the total velocity is 8Km/hr sin (theta)=4/8. To observer ...X---I
ferry is bearing directly at them--he doesn't see the angle....X-,I
the ferry must make with respect to the shoreline since......X
the net velocity upstream is a wash, ie=0. The component
dircted toward the river is then cos(30)*8. Your approach
using pythagorans theorum ok, but should be:

8=sqrt(4^2+Vapperent^2), squaring both sides V^2=64-16

 

[pivoxa15]

I see, the key idea was that the ship is traveling at an angle of 30 degrees upstream. There is a horizontal component of 4km/h directly upstream and a vertical speed directly crossing the shore. This speed can be calculated by the pythagoras theorem sqrt(64-16)=6.93km/h. Note that the book got a) wrong. The angle upstream should be different to the angle the ship would be tilted had it traveled directly straight. Because in one case, 8km/h was the hypotenus, in the other it was not.

 

[denverdoc]

Exactly, complain re the text, there is no excuse for these types of errors.