Question

I think I know how to do these problems just need someone to double check my answers with

1 For the two vectors in the x-y plane, a) Calculate the sum of the vectors (R) by first calculating Rx and Ry (the scalar sums of the x and b) c) y components, respectively) and then writing the vector result R in ijk summation format. Draw the graphical representation of the summation of the two vectors, this should include x-y reference axes, the two original vectors, and the resultant R. Calculate the magnitude of the resultant, Calculate φ , the angle the resultant makes with the x-axis. d) 40° 352.5

Answer 1

There are two vectors in the figure. Let's say the first vector as (having magnitude 3) and the other vector as (having magnitude 2.5).

From the figure, we can write

or,   

= 2.3i + 1.9

And,

or,   

or,

(a) The sum of the vectors :

  

  

  

or,   

R-3.73-0.61

[ Here, R_x = 3.73 and R_y = - 0.61 ]

(b)  The graphical representation can be done by using shifting of vectors.

  

R=A+B 2.5 3 40°

This is known as triangular rule of vector addition . You can also draw it using trapezoidal rule.

(c) Magnitude of vector R Can be calculated as

  

or,  

or,  

or,  

(d) The angle (or ) made by resultant vector with x - axis can be calculated as

  

or,

θ = tan-1 (-0.61 3.73

or,  

Hence, the resultant vector makes -9.28⁰ with positive x - axis or 350.7⁰ (=360 - 9.28) with x - axis in anticlockwise direction.

9.2

For any doubt please comment and please give an up vote. Thank you.