Use the parallelogram rule to find the magnitude of the result...

Question

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.

Accepted Answer

Hey, everyone here, we are asked to calculate the magnitude of the resultant force. Writing our answer in one decimal place. Here we are given a sketch of two force vectors and the angle between them where the left force vector is £24 the bottom vector is £78 and the angle between them is 130 degrees. We have four answer choice options. A £95.2. B £65.2 C £88.7 and D £73.9. So to begin this problem, we want to sketch in our resultant force onto our given sketch. And so we just need to draw an arrow in between directly in between our two already sketched vectors. And now we want to complete the parallelogram by just connecting each head of each arrow by a dash line. Next, we want to label the adjacent angle from our given 130 degree angle as let's say angle theta. And now before we can begin applying the parallelogram rule, we first need to find this adjacent angle. And so for this, we need to recall the supplementary angle property, which tells us that 180 degrees minus our given angle, 130 degrees is equal to the adjacent angle theta. Now, just evaluating, we find that theta is equal to 50 degrees. Now, with our newfound angle, we can apply the parallelogram rule which tells us that the magnitude of our resultant force is equivalent to the square root of 24 squared plus 78 squared minus two, multiplied by 24 multiplied by 78 multiplied by cosine of 50 degrees. And so now we just want to evaluate this expression. And so we find that the magnitude of our resultant force is approximately 65.218120. And now we just need to round to the nearest 10th. And so the magnitude of our resultant force is approximately equal to £65.2. And with this rounded value, we are left with answer choice B where again, our final answer is £65.2. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Use the parallelogram rule to find the magnitude of the resultant force for the two forces shown in each figure. Round answers to the nearest tenth.
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Key Concepts

Parallelogram Rule for Vector Addition

Vector Magnitude Calculation Using Law of Cosines

Rounding and Precision in Final Answers

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