Question

A vector having magnitude 100 unit makes an angle 60° with the horizontal. calculate it's horizontal and vertical component?​

Answer 1

Solution:

(refer to the given attachment)

Finding horizontal component:

From the figure,

X axis forms the horizontal component.

So, the horizontal component would be

$= \bf{100 \: \: cos \: 60^{ \circ} }$

$= \sf{100 \times \dfrac{1}{2} }$

$= \boxed{ \sf{50 \: units} }$

Now, vertical component:

$= \sf{100 \: \: sin \: {60}^{ \circ} }$

$= 100 \times \dfrac{ \sqrt{3}}{2}$

$= \boxed{ \sf{50 \sqrt{3} \: units}}$

Therefore,

• Horizontal component = 50 units
• Vertical component = 50√3 units

General misconception:

Usually students assume that horizontal component is always cos θ and vertical component is always sin θ which is WRONG.

Correct logic:

• The component (line) where the vector makes an angle θ is the cos θ.
• Here, the vector forms 60° angle with X axis and hence horizontal component is considered as cos θ.
• Then, the vertical component will obviously be sin θ.
• Suppose, If the vector had formed 60° angle with Y axis, then the horizontal component would have been 100 × sin 60°