Question

Two trains leave the station at t=0 and travel with constant velocity V along straight tracks that make an angle Theta.
a) show that the trains are separating from each other at a rate of v(sqrt(2-2cosTheta))
b)What does this formula give for Theta=pi?

Answer 1

v=constant a=0

Answer 2

\[x=vt\]
for both cars

Answer 3

angle between both cars 180-theta

Answer 4

\[r^2=2(vt)^2-2(vt )^2\cos (\pi -\theta)\]

Answer 5

when v= pi cos pi=-1 which gives 2v as the result

Answer 6

\[r=\sqrt{(vt)^2(2+2\cos \theta )}= vt \sqrt{2+2\cos \theta} \]
\[dr/dt=v=r/t\]

Answer 7

\[v=\frac{ vt \sqrt{2+2\cos \theta}}{ t }=v \sqrt{2+2\cos \theta}\]

Answer 8

\[v \sqrt{2+2\cos \pi}=v \sqrt{2+2(-1)}=0\]