Question

Hopefully x-component and the y- component number (in m) of the vector with magnitude 26.0 and direction 45.0X= mY= m

Answer 1

We are asked to determine the components of a vector that has a magnitude of 26 and a direction of 45 degrees. A diagram of the vector is the following:

We notice that the vector and its components form a right triangle where the magnitude of the vector is the hypotenuse and the y and x components are the sides.

First, we will determine the x-components using the trigonometric function cosine, which is defined as:

`\cos \theta=(adjacent)/(hypotenuse)`

Substituting the values:

`\cos 45=(x)/(26)`

Multiplying both sides by 26 we get:

`26\cos 45=x`

Solving the operations we get:

`18.4=x`

Therefore, the x-component is 18.4 m.

Now, we will determine the y-component using the function sine, which is defined as:

`\sin \theta=(opposite)/(hypotenuse)`

Substituting the values:

`\sin 45=(y)/(26)`

Now, we multiply both sides by 26, we get:

`26\sin 45=y`

Now, we solve the operations:

`18.4=y`

Therefore, the y-component is 18.4 m.