Mathematics 133 -- Intensive Calculus for Science 1
Discussion 4 -- A Balloon Trip with the Montgolfier Brothers
October 17, 2001
Background
One important example of second derivatives comes from the study of
straight line motion. If f(t) represents the position of a
moving object as a function of time, then the first derivative f'(t)
gives the rate of change of position with respect to time or velocity.
The second derivative f ''(t) is the rate of change of velocity
with respect to time, or acceleration. The units of acceleration
are (distance/time)/time, or distance/time2
(for instance miles/hour2 or meters/second2).
The Story
The Montgolfier brothers, Joseph and Etienne, were pioneers in
hot-air ballooning in the late 1700's in France. If they had possessed
appropriate instruments, they might have left a record of one
of their early experiments as shown in the graph below. The graph
shows the vertical velocityv of their balloon as
a function of time t.
Discussion Questions
Over what time intervals was the balloon rising? Over what intervals
was it falling?
What happened at t = 40? (Think about how a hot-air balloon
works.)
At what time was the greatest altitude achieved on this trip?
Over what intervals was the acceleration positive?
What apparently happened right before t = 60?
Assignment
Group write-ups due in class on Monday, October 22.