A vector representing 200 N is oriented at 46
◦
with the horizontal.
What is the magnitude of its horizontal
component?
Answer in units of
To find the magnitude of the horizontal component of a vector, you need to use trigonometry. In this case, you have a vector of 200 N oriented at an angle of 46° with the horizontal.
The horizontal component can be found by using the cosine function. The formula for the horizontal component is:
Horizontal component = Magnitude of vector * cos(angle)
In this case, the magnitude of the vector is 200 N and the angle is 46°. Plugging these values into the formula, we get:
Horizontal component = 200 N * cos(46°)
To find the cosine of 46°, you can use a scientific calculator or look it up in a trigonometric table. The cosine of 46° is approximately 0.7193.
Now, we can calculate the horizontal component:
Horizontal component = 200 N * 0.7193
Multiplying these values, we get:
Horizontal component ≈ 143.86 N
Therefore, the magnitude of the horizontal component of the vector is approximately 143.86 N.