If two objects travel through space along two different curves, it\'s often impo
ID: 2847129 • Letter: I
Question
If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might intersect, but we need to know whether the objects are in the same position at the same time. Suppose the trajectories of two particles are given by the vector functions
for
Find the values of t at which the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
t =
I made the components equal each other to get t=6 or t=9
9 worked in all three giving me (81,81,81)
This is an online question and it marked me wrong. Can you
help me get the correct answer? Thanks
Explanation / Answer
Just look whether there is a t that fulfills the condition that
x of r1 = x of r2
y of r1 = y of r2
z of r1 = z of r2
In your case, check whether there is a t such that
t^2 = 17t-72
(t-9)(t-8)
Hence two t = 8& 9 exists for the 1st case
From equations 1 and 2, you can conclude
10t-9=15t-54
or
5t = 45
or
t=9
It also satisfy the last equation constraint t^2 = 81
Now check whether this fulfills all the equations above (simply by putting 9 at every place where is says