A bouncy ball bounces to 2/3 of its height when dropped on a hard surface. Suppose the ball is dropped from 20 m.

Question

What is the height of the ball after the 6th bounce? Answer = 1280/729 m OR 1.75 m
What is the total distance travelled by the ball after 10 bounces? 98.6 m

So, I assumed a is 20 since it's the starting point of the ball. I assumed R is 2/3 because it is the common ratio(?). I plugged it into my equation, I used this equation

Sn=a(r^n - 1)/r - 1

Sn=20(2/3^6 - 1) / (2/3) - 1 and I got the wrong answer. I think I used the wrong r value.

Thank you for your help.

Answer 1

Rip I feel bad no one replied to you, but I can tell you u are correct. 20 = a and r = 2/3

To get the first question I used this equation:

tn = a*r^n-1

tn = 20 * 2/3^7-1

tn = 20 * 2/3^6

tn = 1280/79

And for b) lol I have no idea, I'm also looking for answers. But anyway what I assumed I should do is use this formula:

Sn = a(1-r^n)/1-r

Assuming: a = 20 r = 2/3 n=10

I plugged in all the values and did the math, and what I got was 58.95950821 and I just am so confused now:

Sn = 20(1-2/3^10)/1-2/3

Sn = 20(1-1024/59049)/ 1/3

Sn = 20(59049/59049 - 1024/59049) 1/3

Sn = 20(58025/59049)/ 1/3

Sn = 20 (58025/59049 * 3)

Sn = 58.9590821

I don't know if I'm using the wrong equation or if I messed up plugging in but someone plz help lmao

Answer 2

final answers is 1280/79.

Answer 3

yeah the previous answers are correct. the answers on the textbook are wrong