Solving Position Vector Problem: Find Acceleration with |f|^2 = 260 + 64 cos3t

[PJH20]

I really need helpo with this question. I am having to revise over easter for the three week break and i need a solution to this. I have all the past exam papers but the lecturere doesn't have any past paper solutions and his lecture notes are vague. TO top it off i wondered if there were any good books with worked examples and questions?

Here is my problem.

At time t, the position vector of a point P, on a fairground ride is given by:

r(t) = (2cost + cos4t)i + (2sint + sin4t)j m

Find its acceleration, F, at time t. Show that:

|f|^2 = 260 + 64 cos3t m^2s^-4



Ok that's the problem.

Now i have managed to get the velocity by differentiation and then the acceleration which works out to be:

a(t) = (-2cost-16cos4t)i + (-2sint-16sin4t)j

But i can't then get this expression to work out to |f|^2 = 260 + 64 cos3t...


Can anyone help?

 

[matt grime]

What have you found |F|^2 to be? You're missing a 4 from inside the first cos in the post.

 

[PJH20]

It is now corrected.

I got a couple of totally different asnwers to |f|^2 that i reckokn are really wrong.

4cos^2(t) - 256cos^2(4t) + 4sin^2(t) + 256sin^2(4t) Is one of my answers that i think looks halfway there...

 

[matt grime]

I think you need to remember that (x+y)^2 = x^2+2xy+y^2 and not x^2+y^2, and that (-x)^2=x

because you're missing two terms in that answer and there's a minus sign, which could just be a typo.

Remember your trig identities too.