10 km/h at 30 degrees + 15 km/h 270 degreesThe first picture is the steps.The second picture is an example of how to do. Correct me if I'm wrong. ## Vector Worksheet #3**Scale:** 5 units = 1 cm ### Problem 1:Calculate the resultant vector from the following:Vectors: - 10 km/h at 120° - 25 km/h at 180°### Diagram:- The diagram visually represents two vectors and their resultant. - Vector 1 is drawn at 120° from the reference line (horizontal eastward axis).- Vector 2 is drawn at 180°, directly south along the Y axis.- The resultant vector is shown in red, calculated from the addition of Vector 1 and Vector 2.### Calculations:1. **Resolve Vectors into Components** - \( V_{1x} = V_1 \cos(θ_1) = 10 \cos(120°) = 10(-0.5) = -5 \, \text{km/h} \) - \( V_{1y} = V_1 \sin(θ_1) = 10 \sin(120°) = 10(0.866) = 8.66 \, \text{km/h} \) - \( V_{2x} = V_2 \cos(θ_2) = 25 \cos(180°) = 25(-1) = -25 \, \text{km/h} \) - \( V_{2y} = V_2 \sin(180°) = 25 \sin(0) = 0 \, \text{km/h} \)2. **Sum of Components** - \( V_x = V_{1x} + V_{2x} = (-5) + (-25) = -30 \, \text{km/h} \) - \( V_y = V_{1y} + V_{2y} = 8.66 + 0 = 8.66 \, \text{km/h} \)3. **Magnitude of the Resultant Vector** - \( V_r = \sqrt{V_x^2 + V_y^2} = \sqrt{(-30)^2 + (8.66)^2} = \sqrt{900 + 75.0} = \sqrt{975} = 31.2 \, \text{km/h} \)4. **Direction of the Resultant Vector** - \( **If you have two or more vectors and they are not on the x-y axis, you have to use both techniques:**- **Use trig functions for each vector’s components:** \( D_y = D \sin \Theta \) \( D_x = D \cos \Theta \)- **Solve for all x and y components.**- **Find the sum (add) all x components, all y components.**- **Use the Pythagorean theorem:** \( D = \sqrt{D_y^2 + D_x^2} \) - **Solve for theta:** \( \Theta = \tan^{-1} \frac{D_y}{D_x} \)

Name: 10 km/h at 30 degrees + 15 km/h 270 degreesThe first picture is the st
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: 10 km/h at 30 degrees + 15 km/h 270 degreesThe first picture is the steps.The second picture is an example of how to do. Correct me if I'm wrong. ## Vector Worksheet #3**Scale:** 5 units = 1 cm ### Problem 1:Calculate the resultant vector from the f