Question

Two vectors of magnitudes 30 units and 70 units are added to each other. What are possible results of this addition? (section 3.3) 10 units 110 units 50 units 30 units

Answer 1

Answer:

50 units

Explanation:

Given,

• magnitude of the first vector = a = 30 units

• magnitude of the second vector = 70 units

As we know, From the law of vector addition,

Resultant of the addition of the two vectors is,

$\therefor R\ =\ \sqrt{a^2\ +\ b^2\ +\ 2abcos\theta}$

where $\theta$ is the angle between the two vectors

And the value of $cos\theat$ lies between -1 ≤ $cos\theta$ ≥ 1.

For the possible values of the addition of the vectors

Therefore maximum possible value for the addition of the vector gives at the value of $cos\theta\ =\ 1$

$\therefore R_{max}\ =\ \sqrt{30^2\ +\ 70^2\ + 2\times 30\times 70\times 1}\\\Rightarrow R_{max}\ =\ 100 units$

Minimum possible value for the addition of the vectors gives at the value of $cos\theta\ =\ -1$

$\therefore R_{min}\ =\ \sqrt{30^2\ +\ 70^2\ + 2\times 30\times 70\times (-1)}\\\Rightarrow R_{min}\ =\ 40 units$

Hence the possible results of the addition of these two vectors is only 50 units which lies between the 40 units and 100 units.