Question

Vector a has a y-component of +9.60 m and makes an angle of 32.0 degrees counterclockwise from the y-axis. what is the x-component?

Answer 1

To find the x-component of the vector, we can use trigonometry. The x-component is 4.48 m.

Step-by-step explanation:

To find the x-component of the vector, we can use trigonometry. The given information tells us that the vector makes an angle of 32.0 degrees counterclockwise from the y-axis. Since the y-component is given as +9.60 m, we can use the sine function to calculate the x-component. The sine of the angle is equal to the opposite side (x-component) divided by the hypotenuse (magnitude of the vector).

Using the formula: sine(angle) = opposite/hypotenuse, we can rearrange it to solve for the x-component. x-component = hypotenuse * sine(angle).

Plugging in the values: x-component = 8.4 m/s * sine(32.0 degrees) = 4.48 m

Answer 2

For this case we have that the x component can be found using the following trigonometric relationship:
tan (90 + 32) = 9.60 / x
From here, we clear the x component.
We have then:
x = 9.60 / tan (122)
x = -5.99 m
Answer:
the x-component is:
x = -5.99 m