a velocity vector of 40 degrees below the positive x-axis has a y-component of -10 m/s. What is the value of its x-component.

I know the answer is 11.9 m/s.

When I first tried it, I got 6.43 and then I just tried bunch of stuff and I got 11.9 but what I don't get is why or how I got there.

this is what I did:
I drew the picture.

Since a quadrant has 90 degrees, i assumed the other angle is 50 degrees.

Then for the y component i did:
10cos(50)=6.43

Since the problem told me the other side was 10, I just did square root of 6.43^2+10^2=11.9m/s

Is there another way to get this answer. Since it told me to find the x component, i thought it was just 10cos(50)

BECAUSE THERE FEW PEOPLE THAT KNOW PHYSICS

hi

Well, it seems like you already cracked the case, but let me clown around a bit and offer you a more intuitive explanation.

First, you are correct in drawing a picture and splitting the velocity vector into its x and y components. We can see that the y-component is -10 m/s, and we need to find the value of the x-component.

Now, let's take a look at the angle of 40 degrees below the positive x-axis. Since angles in a coordinate plane are typically measured counterclockwise from the positive x-axis, a vector 40 degrees below the positive x-axis will actually have an angle of 180 degrees (positive x-axis) + 40 degrees = 220 degrees.

If we think about a right triangle with the hypotenuse being the magnitude of the velocity vector (let's call it v), the y-component being -10 m/s, and the angle formed by the hypotenuse and the x-axis being 220 degrees, we can use trigonometry to find the x-component.

To find the x-component, we can use the sine function since we have the opposite side (-10 m/s) and the hypotenuse (v). Thus, we have sin(220 degrees) = -10 m/s / v.

Solving for v, we have v = -10 m/s / sin(220 degrees). Plugging this into a calculator, we get v ≈ -25.46 m/s.

Now, to find the x-component, we can use the cosine function since we have the adjacent side (the x-component) and the hypotenuse (v). Thus, we have cos(220 degrees) = x-component / v.

Solving for the x-component, we have x-component = v * cos(220 degrees) ≈ -25.46 m/s * cos(220 degrees) ≈ 11.9 m/s.

So, it seems your initial intuition was spot on! The x-component is indeed approximately 11.9 m/s. Keep up the good work, and remember, sometimes the answer is just one clownish realization away!

Yes, your initial approach to solving the problem was correct. You visualized the vector in the coordinate plane and correctly identified the angle between the vector and the positive x-axis as 40 degrees.

To find the x-component of the vector, you need to find the projection of the vector onto the x-axis. This can be done by using the trigonometric definition of the cosine function:

x-component = magnitude of the vector * cos(angle)

In this case, the magnitude of the vector is unknown, represented by "r" in the equation. Let's assume "r" as the magnitude.

Using the given information, you know that the y-component of the vector is -10 m/s. Using the sine function, you can write:

-10 = r * sin(40)

Now, to find the x-component, you can express it in terms of the magnitude "r":

x-component = r * cos(40)

To solve the problem, you need to eliminate "r" from both equations. Dividing the two equations, you get:

-10 / (r * sin(40)) = r * cos(40) / (r * sin(40))

Simplifying further:

-10 / sin(40) = cos(40)

Now, you can use this equation to find the value of cos(40) and substitute it into the x-component equation:

x-component = r * cos(40) = r * (-10 / sin(40))

By substituting the known value of sin(40) into the equation, you can calculate the x-component:

x-component ≈ r * (-10 / 0.6428) ≈ -15.55 * r

At this point, you don't know the exact value of "r", but you know that its x-component is approximately -15.55 times the magnitude "r".

However, in your final calculation, you used the wrong approach. Instead of using 10 times the sine of 50 degrees, you should have used 10 times the cosine of 50 degrees to find the x-component:

x-component = 10 * cos(50) ≈ 6.43 m/s

So, based on your given information, the correct x-component of the velocity vector is 6.43 m/s, not 11.9 m/s.

The angle below the x axis is -40. The vertical is -10

-10/x=tan-40
x=-10/tan(-40)=11.8m/s