Question

1.A ball is dropped from a height of 2.0, to a floor. After each bounce, the ball rises to 63% of its previous height

What is the total vertical distance the ball has travelled after 5 bounces?

2.An oil produces 25000 barrels of oil durign its first month of production. suppose its production drops by 5% each month

estimate the total production before the well runs dry

Answer 1

1. This depends upon whether you add vertical distance going up and going down. I will assume that is what they mean. It also depends upon whether you stop counting at the end of the fifth bounce.

2.00 m going down the first time
2*2.00*0.63 = 2.52 m going up and down on the first bounce
2*2.00*0.63^2 = 1.59 m going up and down on the second bounce.
etc. You can finish these and add them up yourself

2. 25000*(1 + .95 + .95^2 + .95^3 + ...)

If you don't want to add up a lot of terms, you can use the rule that the sum of this infinite series is
25000*/(1-.95) = ?

Answer 2

thanks

for #1 how did you get 2x2x.63?

Answer 3

Up and down means doubling the distance.
2 x 0.63 m is how far it rises after the first bounce