Train Physics, One dimensional Motion

[johndom33]

Homework Statement

Two trains, each having a speed of 30 miles/hr, are headed at
each other on the same straight track. A bird that can fly 60 miles/hr flies
off one train when they are 60 miles apart and heads directly for the other
train. On reaching the other train it flies directly back to the first train
and so forth. (a) How many trips can the bird make form one train to the
other before they crash? (b) What is the total distance the bird travels?

Homework Equations

x=x_i+v_xt

The Attempt at a Solution

I know part b is 60 miles as the bird is flying at a constant 60mph until the trains crash, at one hour.
Part a is what is getting me, though I am thinking that it is technically an infinite number of trips as the bird always reaches the other train 2/3 of the way between the two, eventually making trips of minuscule distances. The whole reducing objects to a single point and all. Even if I started calculating the position of the trains after each trip the bird makes I would enter into limit territory, where the trains never collide, the just get closer and closer.

Am I just way over thinking this?

Thanks

 

[kuruman]

You are correct in that the number of trips is infinite. However, the distance the bird travels is finite. To find that distance you need to multiply the bird's speed by the time it's flying. So how long has the bird been flying?

 

[johndom33]

The bird has flown a total of 60 miles, the trains crash after 1 hour, found by giving each train a position equation: X=X₀+v_xt, so A=0+30t, B=60-30t, find A=B, 30t=60-30t, t=1hour, then Bird=0+60mph(1hour)= 60 miles.

Thank you for confirming the infinite trips, its been a while since i took physics in high school, and I wasn't sure how literal the prof. was talking.