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

Answer:

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, $7=\sqrt{3^{2}+4^{2}+2\times 3\times 4 Cos\theta }$

49 = 9 + 16 + 24 Cosθ

Cosθ = 1

θ = 0°

Thus, the two vectors are inclined at 0°.

(b) R = 1 m

So, $1=\sqrt{3^{2}+4^{2}+2\times 3\times 4 Cos\theta }$

1 = 9 + 16 + 24 Cosθ

Cosθ = - 1

θ = 180°

Thus, the two vectors are inclined at 180°.

(c) R = 5 m

So, $5=\sqrt{3^{2}+4^{2}+2\times 3\times 4 Cos\theta }$

25 = 9 + 16 + 24 Cosθ

Cosθ = 0

θ = 90°

Thus, the two vectors are inclined at 90°.