vector A has a magnitude of 40m at Angle =225°. if we want to add to A a vector B so as to produce a resultant along the positive x-axis that has a magnitude of 20m, what must be the components of B?

Question

vector A has a magnitude of 40m at Angle =225°. if we want to add to A a vector B so as to produce a resultant along the positive x-axis that has a magnitude of 20m, what must be the components of B?

Answer 1

<40 cos225°,40 sin225°> + <x,y> = <20,0>

solve for x and y separately.

Answer 2

I want the answer to the question above

Answer 3

We need answer

Answer 4

Well, let's break this down, shall we?

First, we have vector A with a magnitude of 40m at an angle of 225°. So if we wanted to represent A in terms of its components, we would have:

Ax = 40m * cos(225°)
Ay = 40m * sin(225°)

Now, we want to add vector B to A in order to produce a resultant along the positive x-axis with a magnitude of 20m. This means that the y-component of the resultant must be zero.

Since the y-component of vector A is Ay, the y-component of vector B must be -Ay in order to cancel out Ay and make the y-component of the resultant zero.

Therefore, the components of vector B are:
Bx = 20m (since the x-component is along the positive x-axis)
By = -Ay (to cancel out the y-component of vector A)

So, the components of vector B are:
Bx = 20m
By = -40m * sin(225°)

I hope that helps, or at least makes you chuckle a bit!

Answer 5

To find the components of vector B, we need to break it down into its horizontal (x-axis) and vertical (y-axis) components.

First, let's find the x-component of vector A. The magnitude of vector A is given as 40m, and the angle is given as 225°. To find the x-component, we can use the cosine function:

x-component of A = magnitude of A * cos(angle of A)

x-component of A = 40m * cos(225°)

Next, we need to find the x-component of vector B. Since the resultant should be along the positive x-axis, the x-component of vector B should be equal in magnitude but opposite in direction to the x-component of vector A.

x-component of B = -1 * (x-component of A)

Now, let's find the y-component of vector B. Since the resultant vector lies along the positive x-axis, the y-component of vector B should be zero.

Therefore, the components of vector B are:
x-component of B = -1 * (x-component of A)
y-component of B = 0

To find the values of the components, substitute the x-component of A into the equation:

x-component of B = -1 * (40m * cos(225°))