Do you know how to calculate velocity vectors from given position vectors?View attachment 13242
I not sure I come to the correct place, but this is my assignment question and I really don't know how to solve it.
you mean differentiation?Do you know how to calculate velocity vectors from given position vectors?
Yes!you mean differentiation?
Va =(-3sin t) i +(4cos t) jYes!
Now tell us:
What are the velocity vectors of particles (1) and (2) at a time 't'?
What are their respective unit vectors?
You need to use the information in the problem to constrain the vectors. Then find t from the resulting equation.Va =(-3sin t) i +(4cos t) j
Vb =(3cos t) i + (-4sin t) j
unit vector of A = ((-3sin t) / (9sin² t + 16cos² t)) i + ((4cos t) / (9sin² t + 16cos² t)) j
unit vector of B = ((3cos t) / (9cos² t + 16sin² t)) i + ((-4sin t) / (9cos² t + 16sin² t)) j
I cannot understand the logic of finding t with these information, what do i miss?
You can see that for vectors Va and Vb, to have opposite directions, we must haveVa =(-3sin t) i +(4cos t) j
Vb =(3cos t) i + (-4sin t) j
unit vector of A = ((-3sin t) / (9sin² t + 16cos² t)) i + ((4cos t) / (9sin² t + 16cos² t)) j
unit vector of B = ((3cos t) / (9cos² t + 16sin² t)) i + ((-4sin t) / (9cos² t + 16sin² t)) j
I cannot understand the logic of finding t with these information, what do i miss?
you mean like this?You can see that for vectors Va and Vb, to have opposite directions, we must have
Va|x = Vb|x and Va|y = Vb|y
for that we need:
sin(t) = cos(t) ..........................................(1)
(1) has multiple solutions. The lowest positive value of 't' to satisfy (1) is
t = ? radian
NO!you mean like this?
-3 sint = 3 cost .......................(1)
4 cost = -4 sint ........................(2)
from (1)
(sin/cos) t = -1
tan t = -1
t = -45
from (2)
(sin/cos) t = -1
tan t = -1
t = -45
so my t is 45?
I still cannot understand, i never done a question like this before, from my understanding in #7 is i use the x axis of vector A = x axis of vector B and same for y axis, from this, make aNO!
Read the response #7 Carefully!
Your work in #8 is very sloppy. You write:
I still cannot understand, i never done a question like this before, from my understanding in #7 is i use the x axis of vector A = x axis of vector B and same for y axis, from this, make a
sin(t) = cos(t) format of equation and use this equation to find t like i did it in #8
My friend tell me the formula should be Va = -VbYour work in #8 is very sloppy. You write:
from (1)
(sin/cos) t = -1
That is not a mathematical expression.
Moreover you write:
tan t = -1
t = -45
What does negative time (=-45) mean? That cannot be correct. Do the arithmetic carefully and correctly!
What is the unit of 't'?
What is the value of "t" - if you measure it in radians?
I was trying to make you realize that the question as written is flawed!
Ask your teacher the question about units.