Question

A force for 100N makes an angle of 60° with y-axis
has horizontal component is: (SAR 2018)
(a) 50N
(b) 60N
(c) 70.7N
(d) 86.6N

Answer 1

The horizontal component of the given 100 N force will be 86.6 N. (option d)

Given,

Force: 100 N,

makes 60° with the y-axis.

To find,

The horizontal component of force.

Solution,

Here, we can see that a force of 100 N is given to be making an angle of 60° with the y-axis.

To find the horizontal component, we need to know its angle with the horizontal or the x-axis.

Here, we can see that the angle made with the y-axis is 60°, and we know that the angle between the x-axis and y-axis is 90°.

So, the angle that 100 N force makes with the x-axis will be

= 90 - 60

= 30°.

Now, the horizontal component of the force is given by

$F_x=F \cos \theta$

As we have found above,

θ = 30°, and,

F = 100 N.

Thus,

$F_x=100 \cos 30\\\implies F_x=100 \times \frac{\sqrt{3} }{2} \\\implies F_x = 50 \times \sqrt{3}\\\implies F_x \approx 50 \times 1.732\\\implies F_x \approx 86.6N$

Therefore, the horizontal component of the given 100 N force will be 86.6 N. (option d)

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