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:

$\cos \theta=\frac{adjacent}{hypotenuse}$

Substituting the values:

$\cos 45=\frac{x}{26}$

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:

$\sin \theta=\frac{opposite}{hypotenuse}$

Substituting the values:

$\sin 45=\frac{y}{26}$

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.