Finding magnitude and direction of resultant force

AI Thread Summary
To find the resultant force from two rocket engines, one producing 725 N forward and the other 513 N at 32.4° above, it is essential to break the forces into their x and y components. The initial attempt incorrectly calculated the magnitude by only considering the x component, leading to an incorrect result of 1158 N instead of the correct 1190 N. The proper method involves using the Pythagorean theorem to combine both the x and y components of the forces. The direction of the resultant force can be determined using trigonometric functions based on the calculated components. Understanding these principles is crucial for accurately solving the problem.
azn4lyf89
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Homework Statement


A rocket fires two engines simultaneously. One produces a thrust of 725 N directly forward, while the other gives a 513-N thrust at 32.4° above the forward direction. Find the magnitude and direction (relative to the forward direction) of the resultant force that these engines exert on the rocket.



The Attempt at a Solution


I tried finding the magnitude by doing 725+513(cos(32.4°)) and got 1158 N but for the answer it says its 1190 N. Did I do something wrong or is the book wrong? And I am not sure how to find the direction after I get the magnitude.
 
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Hi Azn4ly, Well the way I would approch this is break everything up into components, and then add the componets of the vectors together and apply pythags therom. So think about it, break the 725 focre into components and then the 513 force into components. Try using that method :-)
 
azn4lyf89 said:

Homework Statement


A rocket fires two engines simultaneously. One produces a thrust of 725 N directly forward, while the other gives a 513-N thrust at 32.4° above the forward direction. Find the magnitude and direction (relative to the forward direction) of the resultant force that these engines exert on the rocket.

The Attempt at a Solution


I tried finding the magnitude by doing 725+513(cos(32.4°)) and got 1158 N but for the answer it says its 1190 N. Did I do something wrong or is the book wrong? And I am not sure how to find the direction after I get the magnitude.

You only calculated the X component of velocity. You need to factor the Y component in as Galadirith suggested by adding its value through the square root of the squares of the components.
 
I am still having problems with this problem. What formula would I use?
 
susangal04 said:
I am still having problems with this problem. What formula would I use?

Pythagorean Theorem.

RSS - The Root Sum of the Squares.

The x and y components are at right angles and hence for the sides of a right triangle.
The relationship of the sides to the hippopotamus is
a2 + b2 = c2
 
hope this helps
 

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