find magnitude, direction/velocity

Printable View

August 29th 2009, 07:13 PM
Arez

find magnitude, direction/velocity

i am having trouble with these two problems, please someone help

Quote:

An object weighing 258.5 pounds is held in equilibrium by two ropes that make angles of 27.34 degrees and 39.22 degrees, respectively, with the vertical. Find the magnitude of the force exerted on the object by each rope.

i think you need something like $||u||cos(27.34) = ||v||cos(39.22)$ and $||u||sin(27.34) + ||v||sin(39.22) = ||w|| = 258.2$ but im not really sure what to do.

Quote:

A ship is sailing due south at 20 miles per hour. A man walks west (i.e., at right angles to the side of the ship) across the deck at 3 miles per hour. What are the magnitude and direction of his velocity relative to the surface of the water?

i don't know what to do here for the most part.

any suggestions would be helpful.
August 29th 2009, 07:31 PM
TKHunny

For the first...You are on the right track. Check your assumptions and let's see what you get.

For the second...It look slike a Right Triangle to me. Draw the picture. (I'm guessing we should ignore the fact that most ship sides are not all that straight. (Lipssealed))
August 29th 2009, 07:37 PM
luobo

Quote:

Originally Posted by Arez

i am having trouble with these two problems, please someone help

i think you need something like $||u||cos(27.34) = ||v||cos(39.22)$ and $||u||sin(27.34) + ||v||sin(39.22) = ||w|| = 258.2$ but im not really sure what to do.

i don't know what to do here for the most part.

any suggestions would be helpful.

Quote:

i think you need something like $||u||cos(27.34) = ||v||cos(39.22)$ and $||u||sin(27.34) + ||v||sin(39.22) = ||w|| = 258.2$ but im not really sure what to do.

What you did would be correct if you switch $\sin \text{ and } \cos .$

Quote:

A ship is sailing due south at 20 miles per hour. A man walks west (i.e., at right angles to the side of the ship) across the deck at 3 miles per hour. What are the magnitude and direction of his velocity relative to the surface of the water?

Suppose:
East: Positive x
North: Positive y

Quote:

i think you need something like $||u||cos(27.34) = ||v||cos(39.22)$ and $||u||sin(27.34) + ||v||sin(39.22) = ||w|| = 258.2$ but im not really sure what to do.

The man's velocity relative to water is:
$\vec{v} = -3\;\vec{i} - 20\;\vec{j} \text{ (mph) }$

Quote:

A ship is sailing due south at 20 miles per hour. A man walks west (i.e., at right angles to the side of the ship) across the deck at 3 miles per hour. What are the magnitude and direction of his velocity relative to the surface of the water?