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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?

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Yes!you mean differentiation?

Now tell us:

What are the velocity vectors of particles (1) and (2) at a time 't'?

What are their respective unit vectors?

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?

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 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?

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You can see that for vectors VVa =(-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?

V

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

you mean like this?You can see that for vectors V_{a}and V_{b}, to have opposite directions, we must have

V_{a}|_{x}= V_{b}|_{x}and V_{a}|_{y}= V_{b}|_{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

-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?

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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?

Read the response #7 Carefully!

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!

sin(t) = cos(t) format of equation and use this equation to find t like i did it in #8

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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

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.

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.

So my answer should be t = 45

Then the question ask me to find t with seconds as unit

but the outcome from t = 45 is in radian unit

so if i use 45 as my answer for t, my t will be 45 radian but not second

Then I need to confirm with my teacher about the question want to to find t in second or in radian form

U mean this?

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Therefore \(\displaystyle t = \tan^{-1}(1) = \frac{\pi}{4}\) seconds, not 45 seconds.