Question

You travel 50 meters at an angle of 37° North of East.

a. Horizontal component = 50 cos(37°)
b. Horizontal component = 50 sin(37°)
c. Vertical component = 50 cos(37°)
d. Vertical component = 50 sin(37°)

Answer 1

The correct answer is a. Horizontal component = 50 cos(37°).

Step-by-step explanation:

When you travel at an angle, the horizontal and vertical components of your displacement can be calculated using trigonometric functions. In this case, the horizontal component is given by the formula
`\( \text{Horizontal component} = \text{Displacement} * \cos(\text{Angle}) \)`. Substituting the given values, we get
`\( \text{Horizontal component} = 50 * \cos(37°) \)`. Evaluating this expression gives the correct answer for the horizontal component of the displacement.

The angle of 37° north of east indicates that the horizontal component is along the eastward direction. The cosine of an angle in this context represents the ratio of the adjacent side (eastward component) to the hypotenuse (total displacement). Therefore, \( \cos(37°) \) accounts for the proportion of the total displacement that contributes to the eastward direction. Multiplying this by the total displacement of 50 meters gives us the horizontal component.

It's important to note that the sine function is used for the vertical component in such cases, as it represents the ratio of the opposite side (northward component) to the hypotenuse. However, for the horizontal component, as in this scenario, the cosine function is the appropriate choice.