course mth174

A ball is dropped from a height of 10 feet. Each bounce is 3/4 of the height of the bounce before. A.) Find an expression for the height to which the ball rises after it hits the floor for the nth time.

= 10(3/4)^n

B.) Find an expression for the total vertical distance the ball has traveled when it hits the floor for the nth time.

a= 10, x= 3/4

so: 10(1-3/4 ^ n) / (1-3/4)= 40(1-(3/4)^n)

Show that a ball dropped from a height h feet reaches the ground in 1/4sqrt' h

h=1/2(32ft/sec^2)t^2

t^2= h/16 , t= 1/4sqrt'h

b.) show that the ball in problem 28 stops bouncing after

11 seconds (about equal to) (1/4sqrt10 + 1/2 sqrt10 *sqrt[3/4 (1/ (1-sqrt'3/4) ]

This is where I was confused on, showing that the ball will stop bouncing after 11 seconds. Would we need to continue out the series until we reach a bounce that is returning close to zero, since, in theory, it will continue to go on forever?

31) this problem deals with the question of estimating the cumulative effect of tax cuts; basically, a tax cut of 100 million will yield a return back in the economy of 80%, since given the information provided, people save 20% and spend 80%. The question asks you to calculate the total additional spending created by such a tax cut. Its seems likely to use the equation s= a/1-x, with a= 100 million and x= .80, yet my answer came out to 500 million; the book's was 400 million. Where is my error?

I have some more physics questions, but my book isn't with me right now, so I will try to submit those sometime tomorrow night. I took my physics test, one problem gave me a bit of confusion and another. I can retake it easily, but if I made 90 or above I won't. Basically, I just had trouble understanding what way the pulley was position; it involved a cart with a mass attached to it and then suspended over the pulley. My visualizations skills didn't prove to adept. "