Applications of vector algebra to physics

[rugapark]

Homework Statement

A ball of mass 1 kg is acted upon by three forces:
Fl = (2i + 4j - 3k) N, F2 = (-3i - j + 2k) Nand F3 = (i - 5j - k) N.
Determine a vector expression for the acceleration of the particle.
If, at time t = 0, it has position r = (i +j) m and velocity u = (i +3j)m/s, write
down the position vector of the ball at time t. Hence, determine its position and
velocity after 2 seconds.

Homework Equations

The Attempt at a Solution

resultant force & acceleration due to forces:

F_resultant = F₁+F₂+F₃ = -(2j+2k)N

F=ma, m=1kg, therefore a = -(2j+2k)ms^-2


position vector at (t), and velocity and position at t=2:

r(t)=r(0)+ut+$$\frac{1}{2}$$at²

therefore r(t)=(i+j)+(i+3j)-$$\frac{1}{2}$$(j+k)t²

so at t=2,

r(2)=(3i+5j-2k), and v(2)=(i+j-2k)ms^-1


any problems? thanks for all the help always!

 

[Dick]

No conceptual problems. You are being pretty sloppy about putting the numbers into r(t)=r(0)+v(0)*t+(1/2)*a*t^2, though. I'd try that part again.

 

[Architeuthis Dux]

Great job using vector algebra to solve this problem! Your solution is correct and you have shown a good understanding of the concepts involved. Keep up the good work! Applications of vector algebra to physics are essential in understanding and analyzing the motion of objects in space. By breaking down forces into their respective components and using vector addition, we can determine the resultant force acting on an object and its resulting acceleration. This is crucial in many areas of physics, such as mechanics and electromagnetism. Your solution also demonstrates the use of kinematic equations to determine the position and velocity of an object at a given time. This is another important application of vector algebra in physics. Good job overall!