A rocket fires two engines simultaneously. One produces a thrust of 755 directly forward while the other gives a thrust of 525 at an angle 24.2above the forward direction. a) Find the magnitude of the resultant force which these engines exert on the rocket.b) Find the deviation of the direction (relative to the forward direction) of the resultant force which these engines exert on the rocket.

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anonymous · Answer

This is my first post on here and I must warn you I am not a specialist. However in my basic studies of forces this could be solved using either complex numbers or drawing out your forces with graph paper. I prefer the complex numbers method. So the first force in polar form would be 755<O degrees. Which in cartesian is 755+i0 or j0 depending on what subject you are doing. Then the second force is 525<24.2 degrees. This in cartesian form is 478.86+i205.21. This is worked out using trigonometry where 525 is your hypotenuse and 24.2 degrees is your internal angle. Sin24.2*525=opposite=i number (y axis(= 215.21. Cos24.2*525=adjacent=real number (x axis)=478.86.

So your two cartesian form numbers are (755+i0) + (478.86 +i215.21).
The addition of like numbers gives you 1233.86+i215.21. This is in cartesian form.
However to translate back to polar you just use pythagorus's theorem and trigonometry again. √(1233.86^2+215.21^2)= 1250.808 this is your resultant force.
To find the angle you just use the tangent inverse function of the opposite/adjacent.
Tan^-1(215.21/1233.86)=9.894 degrees.

Thus your resultant force would be 1250.808 at 9.894 degrees from the original direction. However you want to express this I don't know. However as far as the maths side of it hopefully that helps. I was just passing through and was intrigued.
:)

anonymous · Answer

thank you