Question

What are Superman's x and y components?
30 degrees
100 m

Answer 1

x-component = 50√3

y-component = 50

Step-by-step explanation:

Two-dimensional vectors consist of two components which are x-component and y-component. The vector equation can be written as:

`\displaystyle{ \vec v = x \hat i + y \hat j}`

Each components also can be written in trigonometric form:

`\displaystyle \vec v \\ \displaystyle \sin \theta`

The absolute of vector is called magnitude of vector which is already given in the problem (100 m). The measurement or theta is also given as well, therefore:

`\displaystyle{x = 100 \cos 30 \degree } \\ \displaystyle{y = 100\sin 30 \degree}`

Then evaluate, we have to know that sin30° is 1/2 and cos30° is √3/2.

`\displaystyle{x = 100 * ( √(3))/(2) } \\ \displaystyle{y = 100 * (1)/(2)}`

Therefore, the components are:

`\displaystyle{x = 50 √(3) } \\ \displaystyle{y = 50}`