How Do I Find Vector Components Using Trigonometric Formulas?

[meganw]

Vector Angle Problem - Answered, thanks! =)

1. The problem statement

Find Vector Components

Homework Equations

trig formulas are important here: sin =o/h, cos=a/h, tan=o/a

The Attempt at a Solution

Thanks for the help! =)

 

[neutrino]

Is 7.6 the initial vertical velocity? Or horizontal? Sorry I'm just confused.

It's just initial velocity, which has both vertical and horizontal components.

 

[meganw]

But how do I find those components if I don't know the angle?

 

[neutrino]

Just assign the angle some name, like $\theta_0$. Then with the given info and the equations of motion, solve for $\theta_0$.

 

[meganw]

Thank you so much!

 

[learningphysics]

Thank you so much! I didn't realize I could do that sort of thing...thanks again! =)

Is there any "physics" reason why there are 2 angles...mathematically sin x = 1.5 at various values of x...

sin x must be between 0 and 1...

Actually there's one way to think about why there are two angles... Think about the range when the angle is 0 and the angle is 90... in both cases the range is 0. so the range gets larger as you go up from 0... and as you go down from 90... so that gives an intuitive reason why there are two angles for each range... for a particular range... if you have an angle close to 0... then there's another angle close to 90...

When you solve for $$\theta_0$$ two solutions will appear... note: you're restricted to angles between 0 and 90.

 

[neutrino]

Is there any "physics" reason why there are 2 angles...mathematically sin x = 1.5 at various values of x...

I do not know the "physical reason" behind it. But since we are talking about angles and distances, I guess I will resort to saying "the math works that way." :)

 

[meganw]

Wow, thanks both of you! I really appreciate it, you have no idea! =)