Expert: Abe Mantell - 2/6/2005

Question
Hello Professor Mantell,

I'm taking a History of Mathematics class and I'm working on a few math problems that I'm having trouble with.  I am hoping that you can offer me some help, please.

Here are the questions:

Suppose a ball is thrown downwards at the rate of 40 feet per second from the ground from a height of 600 feet.

A) What are the formula describing distance fallen and velocity?  ( I thought the formulas might be d= 16t^2 +  40t, and v=32t + 40, although I'm not sure what to do about the 600 feet).
B)  After how many seconds does the ball strike the ground?
C)  At what speed is the ball falling at the moment of impact?

I'd appreciate it very much if you could explain how to arrive at the answers.  And thank you for your time!

Thanks,

Sita

Answer
Hello Sita,

A) D(T)=(1/2)gT^2+VoT+Do
-- where g is about -32, Vo=-40, Do=600
-- so, D(T)=-16T^2-40T+600

B) Just solve D(T)=0 for T...to get T=5 sec.

C) speed=D'(T)=D'(5)=-32T-40 for T=5, speed=-200 ft/sec
-- the "-" sign just means "downward"

OK?

Abe