Answer:
To find the magnitude of the vector sum, we can use the Pythagorean theorem. The magnitude (M) is given by the equation: M = sqrt((x-component)^2 + (y-component)^2)
Plugging in the values, we have:
M = sqrt((7.50)^2 + (4.99)^2) = sqrt(56.25 + 24.90) = sqrt(81.15) ≈ 9.01 meters.
Therefore, the magnitude of the vector sum A⃗ + B⃗ is approximately 9.01 meters.
Explanation:
Vector A⃗ is directed along the negative y-axis and has a length of 8.00 meters. Since it is directed downward, its y-component is -8.00 meters and its x-component is 0.
Vector B⃗ is located in the first quadrant, making an angle of 30.0 degrees with the positive y-axis. To find its components, we can use trigonometry. The angle between vector B⃗ and the x-axis is 90 - 30 = 60 degrees.
The x-component of vector B⃗ can be found by multiplying its length (15.0 meters) by the cosine of 60 degrees: x-component = 15.0 * cos(60) = 15.0 * 0.5 = 7.50 meters.
The y-component of vector B⃗ can be found by multiplying its length (15.0 meters) by the sine of 60 degrees: y-component = 15.0 * sin(60) = 15.0 * 0.866 = 12.99 meters (rounded to two decimal places).
Now, let's find the vector sum A⃗ + B⃗ by adding their x-components and y-components separately.
The x-component of the vector sum is 0 + 7.50 = 7.50 meters.The y-component of the vector sum is -8.00 + 12.99 = 4.99 meters (rounded to two decimal places).
