Question

Two vectors, of magnitudes 20 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant?a. 10 mm
b. 20 mm
c. 40 mm
d. 80 mm

Answer 1

Option C is the correct answer.

Explanation:

The magnitudes of two vectors are 20 mm and 50 mm.

Maximum magnitude will be getting when they are acting in the same direction,

   Maximum magnitude = 20 + 50 = 70 mm

Minimum magnitude will be getting when they are acting in the opposite direction,

   Minimum magnitude = 50 - 20 = 30 mm

So the resultant of these two vectors lies in between 70 mm and 30 mm.

Only option C 40 mm satisfies this.

Option C is the correct answer.

Answer 2

The only possible value for the magnitude of the resultant vector is 40 mm.

The given parameters;

• magnitude of the two vectors, 20 mm and 50 mm

If the angle between the two vectors is 90⁰. The resultant of the two vectors is obtained by drawing the vectors at right angle to each. The hypotenuse side of the right triangle becomes the resultant of the two vectors.

Generally, when the angle between the two vectors are not 90⁰, the resultant of the two vectors is calculated as follows;

$R^2 = (50)^2 + (20)^2 \ - \ 2(50 \times 20) \times cos (\theta)$

when θ = 0⁰

The minimum resultant vector is calculated as;

$R^2 = (50)^2 + (20)^2 \ - \ 2(50 \times 20) \times cos (0)\\\\R^2 = 900\\\\R = \sqrt{900} \\\\\R = 30 \ mm$

when θ =  90⁰

The maximum resultant vector is calculated as;

$R^2 = (50)^2 + (20)^2 \ - \ 2(50 \times 20) \times cos (90)\\\\R^2 = 2900\\\\R = \sqrt{2900} \\\\\ R = 53.85 \ mm$

The resultant of the two vectors is between 30 mm and 53.85 mm

The only value between this range is 40 mm.

Thus, the only possible value for the magnitude of the resultant vector is 40 mm.

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