Question

The magnitudes of each of the two displacement vectors r1 and r2 are equal to 47.0...

The magnitudes of each of the two displacement vectors r1 and r2 are equal to 47.0 m. Determine the smallest angle between the two vectors in order for the magnitude of the sum of the two vectors (r1 + r2) to be 29 times greater than the magnitude of the difference of the two vectors (r1 − r2).

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Homework Answers

Answer #1

Given :

r1 = r2 = 47 m ;  

(r1 + r2) = 29 (r1 -r2)

Solution :

According to the magnitude of sum of two vectors can be computed as :

Magnitude of difference of two vectors can be computed as :

As given :

(r1 + r2) = 29(r1 - r2)

  

(47)2 +(47)2 +2(47)(47)cos = 841(472+472) - 1682(47)(47)cos

(3719956)cos = 3711120

  

= 3.95°

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