If two objects travel through space along two different curves, it\'s often impo
ID: 2856712 • 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.
r1(t) = <t2, 12t 32, t2> r2(t) = <17t 72, t2, 11t 24> for t 0.
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.)
Explanation / Answer
given r1(t) = <t2, 12t 32, t2> r2(t) = <17t 72, t2, 11t 24>
equate thre respective coordinates
x coordinates:
t2=17t-72
=>t2-17t+72 =0
=>(t-8)(t-9)=0
=>t=8,t=9
y coordinates:
12t-32=t2
=>t2-12t+32 =0
=>(t-4)(t-8)=0
=>t=4,t=8
z coordinates:
t2=11t-24
=>t2-11t+24 =0
=>(t-3)(t-8)=0
=>t=3,t=8
t=8 is common in all solutions
so object are in same position for t=8, so they collide when t=8