anonymous
  • anonymous
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ganeshie8
  • ganeshie8
add the forces component by component
ganeshie8
  • ganeshie8
|dw:1378540867294:dw|
ganeshie8
  • ganeshie8
|dw:1378540917724:dw|

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More answers

anonymous
  • anonymous
30 by 100 vector, x = 30 cos(100). y = 30sin(100)
anonymous
  • anonymous
25 by 10 vector, x = 25 cos(10). y = 25sin(10)
ganeshie8
  • ganeshie8
perfect !
ganeshie8
  • ganeshie8
now add them component by component :- add x components, add y components
anonymous
  • anonymous
@Loveiskey18:you know the answer !:)
ganeshie8
  • ganeshie8
resultant force = = <30cos(100) + 25cos(10), 30sin(100) + 25sin(10)>
ganeshie8
  • ganeshie8
thats the resultant force vector, can u find its magnitude ? (use calculator)
anonymous
  • anonymous
Magnitude: 103.08lb
ganeshie8
  • ganeshie8
nopes, try again.
ganeshie8
  • ganeshie8
here is the magnitude :- http://www.wolframalpha.com/input/?i=sqrt%28%2830cos%28100%29+%2B+25cos%2810%29%29%5E2%2B%28+30sin%28100%29+%2B+25sin%2810%29%29%5E2%29
ganeshie8
  • ganeshie8
Magnitude : 39.05lb can you find direction ?
anonymous
  • anonymous
So, it's 39?
ganeshie8
  • ganeshie8
yes, to two decimal places it wud be 39.05lb
ganeshie8
  • ganeshie8
Next, find the direction.
anonymous
  • anonymous
1.05.
ganeshie8
  • ganeshie8
direction is nothing but the angle, so just u need to find the angle that the vector makes
ganeshie8
  • ganeshie8
direction = 1.05 degrees is \(\large \color{red}{\checkmark}\)
ganeshie8
  • ganeshie8
http://www.wolframalpha.com/input/?i=arctan%28%28+30sin%28100%29+%2B+25sin%2810%29%29%2F%2830cos%28100%29+%2B+25cos%2810%29%29%29
ganeshie8
  • ganeshie8
good work !!
ganeshie8
  • ganeshie8
hey 1.05 is in radians, it should be 60.19 degrees !!!!!
anonymous
  • anonymous
For the third time, Thank You. You have really been a great help. I really do appreciate it.
ganeshie8
  • ganeshie8
np :) you're wlcme =))

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