A superball that rebounds 3/10 of the height from which it fell on each bounce is dropped from 38 meters. ?

How high does it rebound, in meters, on the 8 th bounce?
How far does it travel, in meters, before coming to rest?

Answer 1

#8# th bounce, height = #38(3/10)^8# distance traveled to rest = #70.5714#

The sequence of heights after leaving is #38{1,3/10,(3/10)^2,(3/10)^3,...,(3/10)^8,...,(3/10)^n}# The space #d# traveled is given by #d=2times 38{1+3/10+(3/10)^2+(3/10)^3+...+(3/10)^n}-38# Now using the polynomial identity #(1-x^{n+1})/(1-x)=1+x+x^2+x^3+...+x^n# #1+3/10+(3/10)^2+(3/10)^3+...+(3/10)^n= (1-(3/10)^{n+1})/(1-(3/10))# Supposing that #n->infty#, then #(3/10)^{n+1}->0# because #(3/10)<1# So we get #1+3/10+(3/10)^2+(3/10)^3+...+(3/10)^n+...= 1/(1-(3/10)) = 10/7# Finally putting all together #d = 2 times 38 times 10/7 -38 = 70.5714#
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Answer 2

The height of the superball after each bounce can be calculated using the formula:

[h_n = \left(\frac{3}{10}\right)^n \times 38]

Where: (h_n) = height after the (n)th bounce (n) = number of bounces

Substituting the values given:

[h_n = \left(\frac{3}{10}\right)^n \times 38]

For example, if we want to find the height after the 5th bounce:

[h_5 = \left(\frac{3}{10}\right)^5 \times 38]

You can use this formula to calculate the height after any specific bounce.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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