Question

What displacement at an angle 60 to x-axis has an x-component of 5m? I cap and j cap are unit vectors in x and y directions, respectively.

Answer 1

Dear Student,

◆ Answer -

5i + 5√3j m.

● Explaination -

# Given -

a = 5 m

θ = 60°

# Solution -

Let a & b be x-component & y-component of supposed displacement vector.

s = ai + bj

Y-component of displacement is given as -

b = |s|.sinθ

b = √(a²+b²) × sin60°

b² = (a²+b²) × sin²60°

b² = (5²+b²) × (√3/2)²

b² × 4/3 = (5²+b²)

4b²/3 - b² = 25

b² × 1/3 = 25

b² = 75

b = 5√3 m

Therefore, displacement vector will be 5i + 5√3j m.

Thanks dear.