A vector has a magnitude of 3.50m and points in a direction that is 145 degree counter wise from the x-axis. find the x and y components
x-component ... 3.50 m * cos(145º)
y-component ... 3.50 m * sin(145º)
Well, let's break it down, shall we? If the magnitude of the vector is 3.50m, then imagine you're dealing with a 3.50m-long arrow. And if it's pointing 145 degrees counterclockwise from the x-axis, it's basically tilted towards a certain direction.
To find the x and y components, let's use a little trigonometry. The x component is found by multiplying the magnitude by the cosine of the angle, and the y component is found by multiplying the magnitude by the sine of the angle. So, here's how it looks:
x component = 3.50m * cos(145°)
y component = 3.50m * sin(145°)
I could give you the exact numerical values, but let's leave a little bit of math fun for you. So, go ahead, grab your calculator, and calculate those values! Don't worry, math won't bite....hopefully!
To find the x and y components of a vector, we can use trigonometry. Let's call the x-component of the vector "Vx" and the y-component "Vy".
We have the magnitude of the vector, which we'll call "V", given as 3.50m. We also have the angle that the vector makes with the x-axis, which is given as 145 degrees.
The x-component, Vx, can be found by multiplying the magnitude of the vector (V) by the cosine of the angle (θ):
Vx = V * cos(θ)
Substituting the given values, we have:
Vx = 3.50m * cos(145°)
Calculating this value using a calculator, we get:
Vx ≈ -2.78m (rounded to two decimal places)
The y-component, Vy, can be found by multiplying the magnitude of the vector (V) by the sine of the angle (θ):
Vy = V * sin(θ)
Substituting the given values, we have:
Vy = 3.50m * sin(145°)
Calculating this value using a calculator, we get:
Vy ≈ 2.90m (rounded to two decimal places)
Therefore, the x-component of the vector is approximately -2.78m and the y-component is approximately 2.90m.
To find the x and y components of a vector, we can use trigonometry.
Given:
Magnitude (r): 3.50 m
Angle (θ): 145 degrees (counterclockwise from the x-axis)
The x component (rx) and y component (ry) can be calculated using the following equations:
rx = r * cos(θ)
ry = r * sin(θ)
Substituting the given values:
rx = 3.50 m * cos(145 degrees)
ry = 3.50 m * sin(145 degrees)
Using a calculator, we can find:
rx = -2.61 m (rounded to two decimal places)
ry = 2.87 m (rounded to two decimal places)
Therefore, the x component is approximately -2.61 m and the y component is approximately 2.87 m.