Calculating Vertical Distance & Tree Age | Geometric Question Solution

[Suy]

Homework Statement

1)A hard rubber ball is dropped from a moving truck with a height of 5 m. The ball rises of the height from which it fell after each bounce. the total vertical distance the ball has traveled at the moment it hits the ground for the eighth time, to the nearest tenth of a meter.

answer is 36.6m

A tree grows 1.5 m during the first year of planting. durring each subsequent year, the tree grows 9/10 of the previous year's growth. when the growth of the tee since planting is 11.35 m , its age is
a)4.8 yrs
b)12 yrs
c)13 yrs
d)15 yrs

Homework Equations

ar^n-1

a(r^n-1)
r-1

The Attempt at a Solution

The first question, I not sure how to get the ratio, is it 1?


2) 1.5(1.9)^n-1=11.35
n=4.2
Not sure what i did wrong..
ty..

 

[Mark44]

In the first problem, you are missing the ratio in your problem description.

The ball rises of the height from which it fell after each bounce.

This is probably not something you are to figure out, but is instead, information given in the problem.

What is the exact problem statement?

 

[Suy]

In the first problem, you are missing the ratio in your problem description.
This is probably not something you are to figure out, but is instead, information given in the problem.

What is the exact problem statement?

r=1?
but if it is 1,
5*2*7+5=75

 

[Mark44]

r=1?
but if it is 1,
5*2*7+5=75

r = 1 makes no sense physically, because it is not possible for the ball to rebound back to its original position. There are energy losses due to the impacts with the ground not being perfectly elastic.

The other information in the problem suggests that the ratio is not 1. If it were, the distance it would have traveled by the eighth time it hit the ground would be 5 + 7*5*2 = 75 m. When it hits the ground the first time, the distance traveled is 5 m. The second time, the distance traveled is 15 m. Third time, 25 m., and so on. Each time the ball hits the ground again, the total distance traveled is an integer whose last digit is 5.

Let me say it again: What is the exact problem statement?

 

[willem2]

The equation you need is \sum_0^{n-1} a^n = \frac {a^n - 1} {a-1}


For problem 1, the problem seems to be missing some information. Is 36.6 meter the answer
or part of the problem statement?

For problem 2, a should be equal to 0.9 and not 1.9

 

[Mark44]

For the second question, instead of just blindly plugging numbers into formulas, try using your reasoning powers to come up with an equation that describes the situation.

A tree grows 1.5 m during the first year of planting. durring each subsequent year, the tree grows 9/10 of the previous year's growth. when the growth of the tee since planting is 11.35 m , its age is
a)4.8 yrs
b)12 yrs
c)13 yrs
d)15 yrs

1.5 + 1.5(.9) + 1.5(.9)² + ... + 1.5(.9)ⁿ = 11.35

Solve for n, but you'll have to interpret what n means relative to this problem.

 

[Suy]

i got number 2 now.., but i still don't get 1...
it's doesn't make sense to me...
It's asking for the total vertical distance that the ball traveled, so the second time to total distance is 15.
"When it hits the ground the first time, the distance traveled is 5 m. The second time, the distance traveled is 15 m. Third time, 25 m.,"
like you said the first distance is 5m, and then 5+5+5, third, 5+5+5+5+5
so are you saying that the ball rebound to the original height?
but you said the ball is not perfectly elastic

 

[Mark44]

I'm not saying that the ball rebounds to its original height each time. I'm saying that if we temporarily accept that ball rebounds to its original height each time, the distances would be as I explained, so you couldn't possibly get an answer of 36.6 m. That's a second reason why you should not assume a ratio of r = 1 for this problem.

When you post a problem here, you should post the problem exactly as it's written, otherwise we can't help you out. We shouldn't have to guess at the information given in the problem. This is the second time you have posted a problem with incomplete information.

 

[Suy]

Last time, the question was in the quiz. That's why i couldn't give the exact problem.
But for this one, it's on my worksheet. I typed exactly what the paper say. I don't know what I miss. Also, on the back of paper, the answer is 36.6m.

The equation you need is \sum_0^{n-1} a^n = \frac {a^n - 1} {a-1}For problem 1, the problem seems to be missing some information. Is 36.6 meter the answer
or part of the problem statement?

For problem 2, a should be equal to 0.9 and not 1.9

36.6m is the answer. Probably you are right, the question is missing something.