Answer :
This is a geometric sequence. The first term is the max height of the first curved path, which is 0.5. The second one is 52% of that meaning that it is 0.52 times the first term. The third term is 0.52 times the second term. Thus, in this geometric sequence,
[tex]a = 0.5 [/tex]
[tex]r = 0.52 [/tex]
You will need to use the relation [tex] a_n = a \cdot r^{n-1} [/tex]
[tex]a = 0.5 [/tex]
[tex]r = 0.52 [/tex]
You will need to use the relation [tex] a_n = a \cdot r^{n-1} [/tex]
Answer:
- [tex]f(n)=0.5(0.52)^{n-1}[/tex]
- 0.14 m
Step-by-step explanation:
The initial height of the ball is 0.5 m
Each curved path has 52% of the height of the previous path, i.e the height of the ball after one bounce will be,
[tex]=\dfrac{52}{100}\times 0.5\\\\=0.52\times 0.5\ m[/tex]
The height of the ball after 2 bounces will be,
[tex]=\dfrac{52}{100}\times(0.52\times 0.5)[/tex]
[tex]=0.52\times0.52\times 0.5[/tex]
[tex]=0.52^2\times 0.5\ m[/tex]
Hence the series becomes,
[tex]0.5,0.5(0.52),0.5(0.52)^2,............[/tex]
This is the case of Geometric Progression.
But as it is given that the initial height will be given by n=1, so the rules for finding the height f(n) after n bounces would be,
[tex]f(n)=0.5(0.52)^{n-1}[/tex]
Putting n=3, we can get the height of the ball of the third path,
[tex]\Rightarrow f(3)=0.5(0.52)^{3-1}=0.5(0.52)^{2}=0.14\ m[/tex]
