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
thanks
for #1 how did you get 2x2x.63?
Up and down means doubling the distance.
2 x 0.63 m is how far it rises after the first bounce
To find the total vertical distance the ball has traveled after 5 bounces, we need to calculate the distance it traveled on each bounce and then sum them up.
Considering the given information that after each bounce, the ball rises to 63% of its previous height, we can calculate the distance traveled on each bounce as follows:
First, the ball is dropped from a height of 2.0 units. So, on the first bounce, it reaches a height of 2.0 * 0.63 = 1.26 units.
On the second bounce, it reaches a height of 1.26 * 0.63 = 0.7938 units.
On the third bounce, it reaches a height of 0.7938 * 0.63 = 0.500094 units.
On the fourth bounce, it reaches a height of 0.500094 * 0.63 = 0.31505922 units.
On the fifth and final bounce, it reaches a height of 0.31505922 * 0.63 = 0.1986328806 units.
Now, to find the total vertical distance traveled after 5 bounces, we sum up the heights reached on each bounce:
Total distance = 2.0 + 1.26 + 0.7938 + 0.500094 + 0.31505922 + 0.1986328806
Therefore, the total vertical distance the ball has traveled after 5 bounces is approximately 5.0635861006 units.
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To estimate the total production before the well runs dry, we need to calculate the production for each month until it drops to zero.
Considering the given information that the well produces 25,000 barrels of oil during its first month of production and the production drops by 5% each month, we can estimate the total production as follows:
First, in the first month, the well produces 25,000 barrels.
In the second month, the production drops by 5%. So, the production is 25,000 * 0.95 = 23,750 barrels.
In the third month, the production again drops by 5%. So, the production is 23,750 * 0.95 = 22,562.5 barrels.
We can continue this pattern for each subsequent month, decreasing the production by 5% each time.
So, to estimate the total production before the well runs dry, we need to sum up the production for each month until it drops to zero. Since we don't have information on when the production will reach zero, we can assume it runs infinitely. In this case, we can use the formula for the sum of an infinite geometric series:
Total Production = First Month Production / (1 - (Common Ratio))
In our case, the first month production is 25,000 barrels and the common ratio is 0.95 (1 - 0.05).
Total Production = 25,000 / (1 - 0.95)
Total Production = 25,000 / 0.05
Total Production = 500,000 barrels
Therefore, the estimated total production before the well runs dry is 500,000 barrels.
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) = ?