Velocity vector displacement problem

[Toon]

1.)Hey everyone! I am having some trouble with a problem and hoped someone might be able to steer me in the right direction! The problem states ,
A motorist drives south at 20.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 2.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. Whats the total displacement?

2.) I am assuming we will have to use the equation vector v = sqrt( _i ^2 + _j^2) to find its magnitude.

3.)So I first did sqrt(20^2 + 25^2) to try and calculate the vector made by south and west directions. Then used that answer to calculate the vector made by northwest and west direction however that produced the wrong answer. I have a feeling I am approaching the problem using a wrong method and I am currently lost. Any help?

 

[Stephen Tashi]

I have a feeling I am approaching the problem using a wrong method

If you drive South at a velocity of 20 m/sec for 3.00 minutes, how far are you displaced from your starting point at the end of the 3.00 minutes?

Have you studied how to add vectors by adding their components?

 

[Toon]

If you drive South at a velocity of 20 m/sec for 3.00 minutes, how far are you displaced from your starting point at the end of the 3.00 minutes?

Have you studied how to add vectors by adding their components?

3600 meters? Yeah I haved. So I am assuming I should do the sqrt(__south^2 + ___west^2 + _____northwest^2) to find my displacement?

 

[Stephen Tashi]

3600 meters? Yeah I haved. So I am assuming I should do the sqrt(__south^2 + ___west^2 + _____northwest^2) to find my displacement?

So I am assuming I should do the sqrt(__south^2 + ___west^2 + _____northwest^2) to find my displacement?

That would be crazy.

You have to find the sum of the vectors before you can compute the magnitude of that sum. First, add the vectors to obtain a vector. It will be a vector that has 2 components.

 

[NascentOxygen]

3600 meters? Yeah I haved. So I am assuming I should do the sqrt(__south^2 + ___west^2 + _____northwest^2) to find my displacement?

You are finding the magnitude after vector addition here, yes. Have you learned that formula for a 4-sided triangle, or what?? oo)

 

[Toon]

That would be crazy.

You have to find the sum of the vectors before you can compute the magnitude of that sum. First, add the vectors to obtain a vector. It will be a vector that has 2 components.

So I did sqrt(__sotuh^2 + ___west^2) to obtain the vector. However, I am not quit sure what to do with that vector

 

[NascentOxygen]

Perhaps break all vectors you are summing into their "horizontal" and "vertical" components, then add all the corresponding components.

Only after you have added all vectors this way do you apply Pythagoras, and if required also calculate the angle/direction.

 

[Stephen Tashi]

So I did sqrt(__sotuh^2 + ___west^2) to obtain the vector.

The square root of a number isn't a two dimensional vector.

Do what NascentOxygen suggested.

 

[Toon]

Perhaps break all vectors you are summing into their "horizontal" and "vertical" components, then add all the corresponding components.

Only after you have added all vectors this way do you apply Pythagoras, and if required also calculate the angle/direction.

Ive been trying this method and kinda understand vectors more now, but one thing I am still confusing about is the vector that is going northwest. I'm not sure what its components are.

 

[Stephen Tashi]

Ive been trying this method and kinda understand vectors more now, but one thing I am still confusing about is the vector that is going northwest. I'm not sure what its components are.

What angle does a vector pointing exactly northwest make with the x-axis? Use trigonometry to find it's north and west ( = negative east) components.