Answer to Question #156974 in Classical Mechanics for ana

Question

Consider two vectors A and B. Vector A has a magnitude of 13 and points at an angle of 72 degrees above the +x axis. Vector B has a magnitude of 8 and points at an angle of 31 degrees below the +x axis.

a.     What are the x and y components of vector A?

 

 

 

 

b.     What are the x and y components of vector B?

 

 

 

 

c.     Suppose vector C is defined as C=A+B. What are the x and y components of vector C?

 

 

 

 

d.     What is the magnitude of vector C?

 

 

 

e.     At what angle does vector C point?

Answer 1

Answer

a) What are the x and y component of vector A

$A_x=13cos72^°=4$ unit

$A_y=13sin72^°=12.37$ unit

b) What are the x and y component of vector B

$B_x=8cos31^°=6.86$ unit

$B_y=8sin31^°=4.12$ unit

c) C=A+B so it's components

$C_x=10.86$ unit

$C_y=$ 16.49unit

d) magnitude of C

$C=\sqrt{C_x^2+C_y^2}=19.72$ unit

e) angle

$\theta=tan^{-1}(\frac{C_y}{C_x}) =57^°$