Question

Consider two displacements, one of magnitude 3 m and another of magnitude 4 m. Show how the displacement vectors may be combined to get a resultant displacement of magnitude (a) 7 m, (b) 1 m, and (c) 5 m.

Answer 1

Step-by-step explanation:

A = 3m

B = 4 m

let the angle between the two vectors is θ.

the resultant of two vectors is given by

`R=\sqrt{A^(2)+B^(2)+2ABCos\theta }`

(a) R = 7 m

So,
`7=\sqrt{3^(2)+4^(2)+2* 3* 4 Cos\theta }`

49 = 9 + 16 + 24 Cosθ

Cosθ = 1

θ = 0°

Thus, the two vectors are inclined at 0°.

(b) R = 1 m

So,
`1=\sqrt{3^(2)+4^(2)+2* 3* 4 Cos\theta }`

1 = 9 + 16 + 24 Cosθ

Cosθ = - 1

θ = 180°

Thus, the two vectors are inclined at 180°.

(c) R = 5 m

So,
`5=\sqrt{3^(2)+4^(2)+2* 3* 4 Cos\theta }`

25 = 9 + 16 + 24 Cosθ

Cosθ = 0

θ = 90°

Thus, the two vectors are inclined at 90°.