Find the x- and y-components of the vector d⃗ = (6.0 km , 31 ∘ left of +y-axis).
I worked it out and got 5.14, 3.09 and apparently it's wrong, I don't know what I did wrong.
check your signs. The line is to the LEFT of the y axis.
In this question, the vector makes a 31 degree angle with the y-axis, not the x-axis. Also, remember that the x-value is negative. The correct answer is -3.09, 5.14 km.
Well, it seems like you've made a slight calculation error. Let's find out what happened.
To find the x- and y-components of the vector, we can use trigonometry. The magnitude of the vector, 6.0 km, is the hypotenuse of a right triangle. The angle of 31 degrees is the angle between the vector and the positive y-axis.
To find the x-component, we can use the formula:
x = 6.0 km * cos(31 degrees)
Calculating this, we get:
x = 6.0 km * cos(31 degrees) ≈ 5.14 km
So, it seems like you got the x-component right! Great job on that part.
Now, let's find the y-component. We can use the same formula, but this time we'll use the sine of the angle:
y = 6.0 km * sin(31 degrees)
Calculating this, we get:
y = 6.0 km * sin(31 degrees) ≈ 3.09 km
Ah, there's the slight error! It seems like you made a mistake in evaluating the sine. The correct y-component should be approximately 3.09 km.
So, to summarize:
x-component ≈ 5.14 km
y-component ≈ 3.09 km
Keep up the good work, and don't let those small errors bog you down!
To find the x- and y-components of a vector, you can use trigonometric ratios.
In this case, the vector d⃗ has a magnitude of 6.0 km and is at an angle of 31 degrees left of the +y-axis.
Step 1: Convert the angle to standard position
Since the vector is left of the +y-axis, we need to convert the angle to standard position by subtracting it from 90 degrees (assuming counterclockwise positive).
90 degrees - 31 degrees = 59 degrees
Step 2: Calculate the x-component (horizontal component)
To calculate the x-component, we can use the cosine of the angle:
x-component = magnitude * cos(angle)
x-component = 6.0 km * cos(59 degrees)
x-component ≈ 3.09 km
Step 3: Calculate the y-component (vertical component)
To calculate the y-component, we can use the sine of the angle:
y-component = magnitude * sin(angle)
y-component = 6.0 km * sin(59 degrees)
y-component ≈ 5.14 km
Therefore, the x- and y-components of the vector d⃗ are approximately 3.09 km and 5.14 km, respectively.
It seems that you made a mistake in your calculations. Double-check the trigonometric functions and the angle conversions to ensure accuracy. Also, make sure your calculator is set to the correct angle unit (degrees or radians) for the calculations.