Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

When a ball is dropped onto a flat floor, it bounces to 65% of the height from which it was dropped. If the ball is dropped from 80 cm, construct a sequence consists of the first, second and third term which represents the height of each bounce from the first drop.
13n
Show that the height of nth bounce, Tn is = 80  .
20
Hence, find the height of the fifth bounce


Sagot :

Using a geometric sequence, it is found that:

  • The rule for the height of the nth bounce is:

[tex]a_n = 52(0.65)^{n-1}[/tex]

  • The height of the fifth bounce is of 9.28 cm.

In a geometric sequence, the quotient between consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

In this problem:

  • Bounces to 65% of the height from which it was dropped, thus the common ratio is of [tex]q = 0.65[/tex].
  • Dropped from 80 cm, thus, the height of the first bounce is [tex]a_1 = 80(0.65) = 52[/tex].

Thus, the rule for the height of the nth bounce is:

[tex]a_n = 52(0.65)^{n-1}[/tex]

The height of the fifth bounce is [tex]a_5[/tex], thus:

[tex]a_5 = 52(0.65)^{5-1} = 9.28[/tex]

The height of the fifth bounce is of 9.28 cm.

A similar problem is given at https://brainly.com/question/11847927