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Find the sum of the following vectors graphically and algebraically (It may be necessary to convert the polar coordinates to Cartesian coordinates). Sketch the graph below. Present your algebraic result in polar form to a precision of one decimal place for both magnitude and angle. P1,i = (545 9 cm m/s,44.0°); P2i = (2719 cm/s,136.0°) Pitotal (

Find the sum of the following vectors graphically and algebraically (It may be necessary to convert the polar coordinates to Cartesian coordinates). Sketch the graph below. Present your algebraic result in polar form to a precision of one decimal place for both magnitude and angle. P1,i = (545 9 cm m/s,44.0°); P2i = (2719 cm/s,136.0°) Pitotal (

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# Vector Addition and Polar Conversion ## Problem Statement Find the sum of the following vectors graphically and algebraically. It may be necessary to convert the polar coordinates to Cartesian coordinates. Sketch the graph and present your algebraic result in polar form to a precision of one decimal place for both magnitude and angle. ### Given Vectors: - \(\vec{p}_{1,i} = (545 \, \text{g}\, \text{cm/s}, 44.0^\circ)\) - \(\vec{p}_{2,i} = (271 \, \text{g}\, \text{cm/s}, 136.0^\circ)\) A graph is required to visually represent these vectors and their resultant. ## Graph Description The graph consists of two perpendicular lines representing the axes \(p_x\) and \(p_y\). An empty rectangular box is labeled \(\vec{p}_{i,total}(\,\_,\,\_\,)\), which is intended to be filled with the Cartesian components of the resultant vector sum. ### Steps for Solving: 1. **Convert to Cartesian Coordinates:** - For each vector, calculate the \(x\) and \(y\) components using: - \(x = r \cdot \cos(\theta)\) - \(y = r \cdot \sin(\theta)\) 2. **Sum the Components:** - Add the respective components from both vectors to find the total components: - \(p_{x,total} = p_{1x} + p_{2x}\) - \(p_{y,total} = p_{1y} + p_{2y}\) 3. **Convert Back to Polar Coordinates:** - Calculate the magnitude using: - \(r = \sqrt{(p_{x,total}^2 + p_{y,total}^2)}\) - Find the angle using: - \(\theta = \tan^{-1}(\frac{p_{y,total}}{p_{x,total}})\) 4. **Present the Result:** - Input the magnitude and angle into the box \(\vec{p}_{i,total}(\,\_,\,\_\,)\). Ensure that the calculations are precise to one decimal place for both magnitude and angle. The resultant vector and its direction should be visually represented on the graph in relation to the outlined axes. This ensures a comprehensive
Transcribed Image Text:# Vector Addition and Polar Conversion ## Problem Statement Find the sum of the following vectors graphically and algebraically. It may be necessary to convert the polar coordinates to Cartesian coordinates. Sketch the graph and present your algebraic result in polar form to a precision of one decimal place for both magnitude and angle. ### Given Vectors: - \(\vec{p}_{1,i} = (545 \, \text{g}\, \text{cm/s}, 44.0^\circ)\) - \(\vec{p}_{2,i} = (271 \, \text{g}\, \text{cm/s}, 136.0^\circ)\) A graph is required to visually represent these vectors and their resultant. ## Graph Description The graph consists of two perpendicular lines representing the axes \(p_x\) and \(p_y\). An empty rectangular box is labeled \(\vec{p}_{i,total}(\,\_,\,\_\,)\), which is intended to be filled with the Cartesian components of the resultant vector sum. ### Steps for Solving: 1. **Convert to Cartesian Coordinates:** - For each vector, calculate the \(x\) and \(y\) components using: - \(x = r \cdot \cos(\theta)\) - \(y = r \cdot \sin(\theta)\) 2. **Sum the Components:** - Add the respective components from both vectors to find the total components: - \(p_{x,total} = p_{1x} + p_{2x}\) - \(p_{y,total} = p_{1y} + p_{2y}\) 3. **Convert Back to Polar Coordinates:** - Calculate the magnitude using: - \(r = \sqrt{(p_{x,total}^2 + p_{y,total}^2)}\) - Find the angle using: - \(\theta = \tan^{-1}(\frac{p_{y,total}}{p_{x,total}})\) 4. **Present the Result:** - Input the magnitude and angle into the box \(\vec{p}_{i,total}(\,\_,\,\_\,)\). Ensure that the calculations are precise to one decimal place for both magnitude and angle. The resultant vector and its direction should be visually represented on the graph in relation to the outlined axes. This ensures a comprehensive
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