Question

A man is pulling arolley on a horizontal road with a force of 100N making 45 degrees with the road. What are the horizontal and vertical components of its force?

Answer 1

To find the horizontal and vertical components of the force, we can use trigonometric functions.

Given: Force applied (F) = 100 N Angle with the horizontal (θ) = 45 degrees

The horizontal component of the force (F_horizontal) is given by:

F_horizontal = F * cos(θ)

F_horizontal = 100 N * cos(45°)

Using the value of cos(45°) (which is (√2)/2):

F_horizontal = 100 N * (√2)/2

F_horizontal ≈ 100 N * 0.707 ≈ 70.7 N (rounded to one decimal place)

So, the horizontal component of the force is approximately 70.7 N.

The vertical component of the force (F_vertical) is given by:

F_vertical = F * sin(θ)

F_vertical = 100 N * sin(45°)

Using the value of sin(45°) (which is (√2)/2):

F_vertical = 100 N * (√2)/2

F_vertical ≈ 100 N * 0.707 ≈ 70.7 N (rounded to one decimal place)

Thus, the vertical component of the force is approximately 70.7 N.

Therefore, the horizontal component of the force is 70.7 N, and the vertical component of the force is also 70.7 N.