about the three forces that are acting on to an object and we need to find out the magnitude of the net force the direction of the net force the magnitude of the net acceleration and the direction of the net acceleration I'll just make one simple correction here it has to be an acceleration so I'll just make okay so we have a mass here an object and three forces are acting so this is f1 force this is the f2 force and this is the f3 force and we have chosen this is an x-axis and this is an y-axis and we can choose our own coordinate system so for my convenience I'm just choosing this as my x axis and this is y axis and the angle of all the forces are given with respect to the coordinate system the force is at 4 f1 is at 45 f2 is at 30 and f3 is at 35 degree now in which direction the object will explore moving so in order to answer that first thing we need to do is find out the direction of the net force and the magnitude of the net force so how are we going to do that we're going to use the first we are going to resolve a force into two rectangular components so let's start with this f1 force and this is our exit system x coordinate our x axis and this is our y axis so the X component of this force will be along this direction it bf1 course I'm 40 degree and a long y-component it would be f1 sine 40 45 degree so we have now two forces and we do not need this force the same way we can dissolve this into two components this component again would be f to push sine 30 degree and in this case the force will be downward and this would be F to shine 30 degree and the last we have to resolve this into two components along the this axis because this is now the angle this force would be cosine Y this cosine because again remember the rule of C and C closer to the angle is always cosine so this component is closer to the angle so this would be cosine component F 3 cosine 45 degree and this is further from the angle so this will be sine component sine 35 degree so all the forces is now shown in this diagram and I'll explain one more time so we'll start with f1 ok the f1 has two components f1 cosine 45 degree again Y cosine how do we know that it is cosine because this is the angle which is closer so closer to the angle is cosine and this component will be sine component so this one is f1 sine of 45 degrees which is shown by the the red arrow now for the f2 this is f2 here I have to again the f2 disa as this angle is 30 degree so this angle also this component will be F 2 cosine 30 degree and this one would be - sine 30 degree and always think of this one as a parallelogram okay so a now stop they've they'll think about yourself first how are you going to resolve this force now f3 at this angle is 35 degree this component will be cosine component which is f 3 cosine 35 degree which is given here and this component will be F 3 sine 35 to be so when all the forces has been dissolved into two components to the tempered components then life is so easy then so what are we going to do now now we're going to find out the total forces that is acting along the x axis and we do not nip these forces now but do not leave this force or do not in this force because this forces has been now resolved into two components x and y components so along x axis a lot of positive x-axis we have three forces which is f1 cosine 45 degree we have F 2 cosine 30 degree and F 3 sine 35 degree these three forces these three put these two forces now acting along the positive x axis and this is acting along the negative of x axis so what is the total force then this force plus test sports - this force that is the total force f1 percent 45 f2 cosine 30 degree and - f3 sine 35 degree and we know that my the magnitude of F 1 this is 60 Newton so writing down the 60 Newton cosine 45 degree F 2 is 50 - 50 and F 3 is 40 Newton and and once we do the math just plugging all the values of cosine 45 cosine 30 and 35 for to get the net resultant force along the x-axis this is the portal net force along the x-axis in sixteen point seven nine Newton the same way let's find out what the total force along the y-axis how we're going to do that so along the y-axis again we'll have three forces which is f1 sine 45 plus F 3 cosine 35 minus F 2 shine per typically f2 sine 30 degree is negative because it is acting along the negative y-direction that's what exactly what I have done here f1 sine 45 minus f2 sine 30 degree plus f3 or sign 35 degree so I can't want to want to put all the numbers what it get is this force F Y is 50 point 2 Newton so we have now find out the total have X component and total Y component so if I have to make life a little easier so what I can do now so let's say this is the box so the total x component is this is the force x component and this is the total FY component this is f X and this is the F Y that's all all the forces now can be resolved by kit can be simply used not as an FX and FY force so the total force the total force can be now written as a sista 2.79 that's the X component Y vector what is the I've vector means that is the this force is now acting along the X direction that's what this is telling you this gives the direction or the component and the y component is 50.2 and J vector J vector is telling you this force is acting along the Y direction and this is reader J hat or J cap so this gives the unit the unit vector on the Y direction and this is the unit vector along X direction so we found out the total the force now let's find out if the magnitude of the force the total magnitude so what if the two forces are acting along X direction and along y direction then the total force can be given by by so let's say in this case this is FX force and then we can now return FY force just like this just like that FY then this gives you the total resultant force all right this is FX force and this is FY force and this gives you the total net force and if you look at this it it just looks this is a right angle triangle and this is the the habit news so by Pythagoras through a theorem the the net force can be given by F X square plus FY square and we already have calculated F X is 60 2.79 and FY is 50 point 2 and if I just do the math what you will get is 80 point 4 Newton now let's talk about the direction how do we find out the direction the direction this will be your the direction this is the direction now now let's call this is an angle theta so how do you find out the theta so if you look into this triangle into this triangle the tangent of theta the tangent of theta would be rise over run right in this case is FY and the run is FX that's exactly I've done here tangent of theta is FY over FX FY is given 50 point 2 and FX is 60 2.79 and if I solve for theta using a calculator you will get thirty eight point six degree so that means the object this object will move and this angle along this direction that's that's the direction the object starts moving so under this forces you see three forces are acting on an XY plane and the object would move at an angle thirty eight point six degree it's a closer to this angle so the object will move along this signal okay along this way now it is fairly simple to calculate the net acceleration the magnitude of the net acceleration the acceleration is given by force per unit mass force divided by the mass the force the net force the total force is eighty point four and the mass of this object is given which is 20 kilogram the mass is given 20 kilogram mass so the acceleration would be four point zero two and the direction so you see now this equation now direction of the this is the direction of the acceleration okay so you see that this is the equation force is equal to mass times acceleration and mass is a scalar quantity so the the direction of the acceleration is the same direction as the force and the angle would be 38 160 exactly this angle so the object would the force would be moving or acting along this direction and so is the acceleration so the system will move along this way thirty eight point six degree angle so that's it for this particular problem and again if you have any questions write down your question and the comment section below and if you want me to do another problem on to the superposition of principle or many forces acting onto an object you just write down the questions in the comment section below and at the end do not forget to like share & subscribe the channel thank you very much