Calculate the x-component and the y-component (in m) of the vector with magnitude 18.0 m and direction 55.0°
as usual, for a vector with length r, at an angle θ,
x = r cosθ
y = r sinθ
Why did the vector lose its job? Because it had no direction!
To calculate the x-component and y-component of the given vector, we can use trigonometry.
The x-component is given by the formula: x = magnitude * cos(direction)
The y-component is given by the formula: y = magnitude * sin(direction)
Plugging in the values, we get:
x = 18.0 m * cos(55.0°)
x = 18.0 m * 0.5736
x ≈ 10.327 m
y = 18.0 m * sin(55.0°)
y = 18.0 m * 0.8192
y ≈ 14.747 m
So, the x-component is approximately 10.327 m, and the y-component is approximately 14.747 m.
To calculate the x-component and y-component of a vector, we can use trigonometry.
Given:
Magnitude (magnitude) = 18.0 m
Direction (theta) = 55.0°
The x-component (Vx) can be calculated as:
Vx = magnitude * cos(theta)
Substituting the given values:
Vx = 18.0 m * cos(55.0°)
Calculating the value of cos(55.0°):
Vx = 18.0 m * 0.57357
Vx ≈ 10.324 m
Similarly, the y-component (Vy) can be calculated as:
Vy = magnitude * sin(theta)
Substituting the given values:
Vy = 18.0 m * sin(55.0°)
Calculating the value of sin(55.0°):
Vy = 18.0 m * 0.81915
Vy ≈ 14.745 m
Therefore, the x-component of the vector is approximately 10.324 m and the y-component is approximately 14.745 m.
To calculate the x-component and y-component of a vector, you can use trigonometry and the given magnitude and direction.
First, let's identify the given information:
Magnitude (magnitude) = 18.0 m
Direction (θ) = 55.0°
To find the x-component, we use the cosine function:
x-component = magnitude * cos(θ)
Substituting the given values:
x-component = 18.0 m * cos(55.0°)
Now, let's calculate the x-component:
x-component ≈ 18.0 m * cos(55.0°) ≈ 10.15 m (rounded to two decimal places)
To find the y-component, we use the sine function:
y-component = magnitude * sin(θ)
Substituting the given values:
y-component = 18.0 m * sin(55.0°)
Now, let's calculate the y-component:
y-component ≈ 18.0 m * sin(55.0°) ≈ 14.53 m (rounded to two decimal places)
Therefore, the x-component of the vector is approximately 10.15 m, and the y-component is approximately 14.53 m.