What is the resultant of the vector from this impact?

AI Thread Summary
The discussion revolves around calculating the resultant vector from two people kicking a ball with forces of 215.0 Newtons and 189.0 Newtons at a 210.0-degree angle. Initial calculations were presented, but there were issues with clarity and accuracy, prompting requests for algebraic steps. The correct approach involves using the cosine rule to find the resultant magnitude, which was approximated to 107 Newtons, though significant figures were debated. Participants emphasized the importance of maintaining significant figures consistent with the input data, suggesting a range of possible answers based on variations in the input values. The conversation highlights the complexities of vector addition and the importance of precision in calculations.
j doe
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Homework Statement


two people kick a ball. one of them kicks it with a force of 215.0 Newtons. the other one with 189.0 Newtons. their approach creates a 210.0 degree angle at the point of impact and causes the ball to go in a different direction. what is the resultant of the vector from this impact?

Homework Equations

The Attempt at a Solution


215.0^2 = 46,225.0

189.0^2 = 35,721.0

46,225.0 + 35,721.0 = 81,946.0

2 x 189.0 = 378.0 + 215.0 = 81,270cos(30) = 70,381.88457

81,946.0 - 70,381.88457 = 11,564.11543

√11,564.11543 = 107.5365772 Newtons
 
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It's very hard to reverse engineer your logic from a string of numbers. Please write your steps algebraically.
 
haruspex said:
It's very hard to reverse engineer your logic from a string of numbers. Please write your steps algebraically.
  • magnitude^2=215^2+189^2-2*215*210*cos(30degrees)=61^2N
 
j doe said:
  • magnitude^2=215^2+189^2-2*215*210*cos(30degrees)=61^2N
That was easier to follow (though still not exactly algebraic) but now you seem to have plugged in a wrong number at one point and got a wrong answer.
I agree with your original 107, but you quote too many significant digits. Never quote more in the answer than the form of the input data implies.
 
haruspex said:
That was easier to follow (though still not exactly algebraic) but now you seem to have plugged in a wrong number at one point and got a wrong answer.
I agree with your original 107, but you quote too many significant digits. Never quote more in the answer than the form of the input data implies.
how many significant figures am i suppose to have and how can i tell?
 
j doe said:
how many significant figures am i suppose to have and how can i tell?
Each number you were given was quoted to four significant figures, so use the same in the answer. Usually, you should use the same as the least precise input number, but in reality it is more complicated than that.
If you care to, you can experiment with this. For each of the three numbers given, consider the highest and lowest exact number that is consistent with it. E.g. 210.0 degrees is anything from 209.95 to 210.05. That gives you eight combinations of extreme values, each combination giving a slightly different answer. What is the range of answers that results?
(But this is probably well beyond what you are expected to do here.)
 

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