Help !! Maths c2 question on series and sequence

HEY :P

I was doing this question
When a ball is dropped onto a horizontal floor it bounces such that it reaches a maximum height
of 60% of the height from which it was dropped.

a )Find the maximum height the ball reaches after its fourth bounce when it is initially dropped from 3 metres above the floor.

after 4th bounce,
reaches 3 × (0.6)^4
= 0.3888 m

im confused,is it arithmetic or geometric ,when i tried it i assumed it would be geometric but then the power would be to 3 so im wrong

b) Show that when the ball is dropped from a height of h metres above the floor it travels a total distance of 4h metres before coming to rest.

total distance
= h + 2[0.6h + (0.6)^2
h + (0.6)^3
h + …]
= h + 2 × S∞ of GP, a = 0.6h, r = 0.6
= h + 2 0.6
1 0.6
× h
−
= h + 3h = 4h metres

could someone explain the second part to me as well :tongue:

Thank you ,
i would really appreciate the help as im really confused on this question
:tongue:

Original post by Sadilla

HEY :P

I was doing this question
When a ball is dropped onto a horizontal floor it bounces such that it reaches a maximum height
of 60% of the height from which it was dropped.

a )Find the maximum height the ball reaches after its fourth bounce when it is initially dropped from 3 metres above the floor.

after 4th bounce,
reaches 3 × (0.6)^4
= 0.3888 m

im confused,is it arithmetic or geometric ,when i tried it i assumed it would be geometric but then the power would be to 3 so im wrong

This is fine, it is indeed a geometric progression for the sequence of heights.

After 0 bounces:

3

After 1 bounce:

3\cdot 0.6

After 2 bounces:

3 \cdot 0.6^2

...
After n bounces:

3 \cdot 0.6^n

b) Show that when the ball is dropped from a height of h metres above the floor it travels a total distance of 4h metres before coming to rest.

total distance
= h + 2[0.6h + (0.6)^2
h + (0.6)^3
h + …]
= h + 2 × S∞ of GP, a = 0.6h, r = 0.6
= h + 2 0.6
1 0.6
× h
−
= h + 3h = 4h metres

could someone explain the second part to me as well :tongue:

Thank you ,
i would really appreciate the help as im really confused on this question
:tongue:

When a ball is dropped, it goes down a distance of h metres. So we have

T=h

so far as the total distance. When it bounces, it comes back up to a height

0.6h

before travelling down to the ground a total distance of

0.6h

as well. So the total distance now is

T=h+0.6h+0.6h = h+2h(0.6)

. Similarly, after the second bounce, it will travel a distance of

2\cdot (0.6^2h)

hence we have

T=h+2h(0.6+0.6^2)

and so on.

We are looking at what we get when the ball becomes at rest, ie when we sum all these bounces which yields an infinite sum.

We get:

h+2h(0.6+0.6^2+0.6^3+...)

which we can calculate by the infinite GP sum formula.

(edited 6 years ago)

Reply 2

Sadilla

OP

10

Original post by RDKGames

This is fine, it is indeed a geometric progression for the sequence of heights.

After 0 bounces: 3
After 1 bounce:

3\cdot 0.6

After 2 bounces:

0.3 \cdot 0.6^2

...
After n bounces:

0.3 \cdot 0.6^n

thank you , you said for the 2 bounces it 0.3 x(0.6)^2 but then how comes the 1st bounce was 3x0=0.6 ? so how comes its 3 and then 0.3 ?

Original post by Sadilla

thank you , you said for the 2 bounces it 0.3 x(0.6)^2 but then how comes the 1st bounce was 3x0=0.6 ? so how comes its 3 and then 0.3 ?

Ooops, sorry, got derailed. Fixed now.

Reply 4

Sadilla

OP

10

Original post by RDKGames

Ooops, sorry, got derailed. Fixed now.

its okay ;p , i was also confused as to why the it goes back down the second time its still 2h ?

Original post by Sadilla

its okay ;p , i was also confused as to why the it goes back down the second time its still 2h ?

What are you referring to?

Reply 6

Sadilla

OP

10

Original post by RDKGames

What are you referring to?

when you said before travelling back down and has height 0.6h , how comes it not times by 0.6 as its 60% of that height ?

Original post by Sadilla

when you said before travelling back down and has height 0.6h , how comes it not times by 0.6 as its 60% of that height ?

Because it hasn't bounced yet...

A ball hit the ground, bounces back up to a height of 0.6h then it falls down the same amount of 0.6h before hitting the ground again and bouncing. Get it?

Help !! Maths c2 question on series and sequence

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you