A ball is such that when it is dropped from a height of 1 metre it bounces vertically from the ground to a height of 0.96 metres. It continues to bounce on the ground and each time the height the ball reaches is reduced. Two different models, A and B, describe this.

Model A : The height reached is reduced by 0.04 metres each time the ball bounces.
Model B : The height reached is reduced by 4% each time the ball bounces.

(i) Find the total distance travelled vertically (up and down) by the ball from the 1st time it hits theground until it hits the ground for the 21st time,
(a) using model A, [3]
(b) using model B. [3]

(ii) Show that, under model B, even if there is no limit to the number of times the ball bounces, the total vertical distance travelled after the first time it hits the ground cannot exceed 48 metres. [2]

Question

A ball is such that when it is dropped from a height of 1 metre it bounces vertically from the ground to a height of 0.96 metres. It continues to bounce on the ground and each time the height the ball reaches is reduced. Two different models, A and B, describe this.

Model A : The height reached is reduced by 0.04 metres each time the ball bounces.
Model B : The height reached is reduced by 4% each time the ball bounces.

(i) Find the total distance travelled vertically (up and down) by the ball from the 1st time it hits theground until it hits the ground for the 21st time,
    (a) using model A, [3]
    (b) using model B. [3]

(ii) Show that, under model B, even if there is no limit to the number of times the ball bounces, the total vertical distance travelled after the first time it hits the ground cannot exceed 48 metres. [2]

maths99 · Answer

@inkyvoyd  @bmk614

bmk614 · Answer

What class is this for?

maths99 · Answer

This is for As level maths

bmk614 · Answer

i. a. The formula you need to use is .96-.04x, where x is 21.
   b. Since you taking away 4% you are actually carrying on 96% of the total. The formula that we need to use for this is .96(.96)^x, where x is 21.

bmk614 · Answer

ii. I'm sorry, but I don't know how to prove this.

maths99 · Answer

@phi

phi · Answer

can you do any of this ?

phi · Answer

model A  is an "arithmetic sequence"
have you studied this ?

maths99 · Answer

i have studied simple arithmetic progressions but not this type @phi

phi · Answer

yes, this one seems complicated.
I'm still puzzling over it.

maths99 · Answer

Okay when you've found a solution, please guide me thnx

phi · Answer

here is what it looks like in pictures:
|dw:1461850795930:dw|