i have the equation
r(t) = sin(2t)i + 2cos(t)j where 0<t<2pi
I have to prove that using this equation that the object it describes passes through the origin twice in the time limit. Does this just mean I have to show the values of t that give r(t) = 0? i.e. pi/2 and 3pi/2?
cheers for the help
a further part of this question is asking when are the times that the displacement is perpendicular to the velocity. Clearly one time would be t=0 as the i and j directions are mutually perpendicular to each other. How would i find the others? Is there some way involving dot products?
When you take the dot product:
sin(2t) [2 cos(2t)] - [2 cos t] [2 sin (t)] = 0
and you know that 2 sin(t) cos(t) is sin(2t), right?
Have you learned about the dot product (also called the scalar product)? Do you understand that it's very different to multiplying two scalars ......?
ive got that bit written down but not sure how to interpret in relation to this quesiton.
with regards dot product
i now have that in the case of these equations
a*b=a1b1 + a2b2
taking a to be the velocity components and b to be displacement components
which leads to 2cos(2t)*sin(2t) and -2sin(t)*2cps(t)
is this correct??