Mesquite Trees, Anon.
Thorn Avenue
Lubbock, TX 79414
Dear Calculus Student,
You don't know me - my name is Betty Kant, but you do know my boss, George. He's such a sweet guy and a wonderful boss. I can't imagine anything I'd rather do for a living than measure thorns for him. He tells me that it was you who came with the new measuring technique-I have to tell you that that's made our job a whole lot easier.
Carol is our local bicycle racing star, and on Veteran's Day, she will be in the race of her life. She and her support team are planning the following maneuver on the 15th lap of her 25 lap race:
She will pass the refreshment stand on the 15th lap at a constant velocity k m/sec and continue at that pace. At that instant (t=0 sec.), her support car will start from the refreshment station to accelerate after her, beginning from a dead stop. The support team guarantees that they can accurately pace their car so that their traveled distance will match the function 1/3(10t^2-t^3), where distance is measured in meters. Their plan, carefully calculated by the crew, is that at the instant that the support car catches up to Carol they will match speeds. A crew member will hand Carol a cold drink, and the car will immediately fall behind.
A. How fast should Carol be traveling as she passes the refreshment stand, so that their will be a smooth hand off?
B. How long will it take the support car to catch her?
C. Consider a pair of axes with time measured horizontally and distance vertically. Draw for us a graph that will depict the distance traveled by Carol and by the car plotted on the same axis.
If I could get your answer by Election Day, November 6, we would have time to work it out in practice before the race. I'd really appreciate it!
Sincerely,
Betty Kant