A prediction is a guess based on facts or evidence
Number 1 is D number 2 is C
The resultant of the forces is 29 N. Option D
<h3>What is the resultant force?</h3>
The resultant force is the force that acts in a given direction. Now we have two forces as enumerated in the question.
Thus;
Resultant = √(10)^2 + (20)^2 - [2 * 10 * 20 * cos (60 - 30))
Resultant = 29 N
Thus, the resultant of the forces is 29 N.
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Missing parts;
Two forces of magnitude 10N and 20N act on a body in directions making angles 30° and 60° respectively with x-axis what is the resultant force
A.17N
B. 19N
C. 23N
D. 29N
E. 37N
This is a classic example of conservation of energy. Assuming that there are no losses due to friction with air we'll proceed by saying that the total energy mus be conserved.
![E_m=E_k+E_p](https://tex.z-dn.net/?f=E_m%3DE_k%2BE_p)
Now having information on the speed at the lowest point we can say that the energy of the system at this point is purely kinetic:
![E_m=Ek=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=E_m%3DEk%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
Where m is the mass of the pendulum. Because of conservation of energy, the total energy at maximum height won't change, but at this point the energy will be purely potential energy instead.
![E_m=E_p](https://tex.z-dn.net/?f=E_m%3DE_p)
This is the part where we exploit the Energy's conservation, I'm really insisting on this fact right here but it's very very important, The totam energy Em was
![E_M=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=E_M%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
It hasn't changed! So inserting this into the equation relating the total energy at the highest point we'll have:
![E_p=mgh=E_m=\frac{1}{2}mv^2](https://tex.z-dn.net/?f=E_p%3Dmgh%3DE_m%3D%5Cfrac%7B1%7D%7B2%7Dmv%5E2)
Solving for h gives us:
![h=\frac{v^2}{2g}.](https://tex.z-dn.net/?f=h%3D%5Cfrac%7Bv%5E2%7D%7B2g%7D.%20)
It doesn't depend on mass!