Question

Find the magnitude of the sum of a 10m displacement and a 5 -m displacement when the angle between them is 45

Answer 1

The magnitude of the resultant of the two vectors is 7.37 m.

Step-by-step explanation:

let the first vector = a = 10 m

let the second vector = b = 5 m

angle between the two vectors, θ = 45⁰

The magnitude of the resultant of the two vectors is calculated as;

`R^2 = a^2 + b^2 -2ab * cos(\theta)\\\\R^2 = 10^2 + 5^2 - [2* 10 * 5 * cos(45)]\\\\R^2 = 125 - [100 * 0.7071]\\\\R^2 = 125 -70.71\\\\R^2 = 54.29 \\\\R= √(54.29) \\\\R = 7.37 \ m`

Therefore, the magnitude of the resultant of the two vectors is 7.37 m.