Question

Haziq drops a ball from a height of H cm above the floor.After the 1st bounce,the ball reaches a height of h_1 cm where H_1=2(H)/3.After the 2nd bounce,the ball reaches a height of H_2 cm where H_2=2(H_1)/3.The ball continue bouncing in this way until it stops.
Given that H=600cm,find
a) the number of bounces when the maximum height of the ball from the floor is less than 100 cm for the first time. @tkhunny

Answer 1

This is my working...maybe u could check my working whether is it correct or not\[a=\frac{ 2 }{ 3 }(600)=400cm~and~r=\frac{ 2 }{ 3 }\]\[T_n<100\]\[400(\frac{ 2 }{ 3 })^{n-1}<100\]\[(\frac{ 2 }{ 3 })^{n-1}<\frac{ 1 }{ 4 }\]\[(n-1)\log_{10}\frac{ 2 }{ 3 }<\log_{10}\frac{ 1 }{ 4 }\]\[n-1<3.419\]\[n<4.419\]\[n=4\]

Answer 2

@tkhunny

Answer 3

600(2/3) = 400 - 1st Bounce
400(2/3) = 266 2/3 - 2nd Bounce
266 2/3(2/3) = 177 7/9 - 3rd Bounce
177 7/9(2/3) = 118.518518... - 4th Bounce
118.518518...(2/3) = 79ish - 5th Bounce

Where did you wander off?

Answer 4

so this mean n=5

Answer 5

Thank you @tkhunny

Answer 6

You did not yet find your error. It's there. Look harder.

Answer 7

Can u show me what error i did in my working pls?
is it the symbol?

Answer 8

This is the first incorrect step:

\(n - 1\;<\;3.419\)

Answer 9

Thank you @tkhunny :) :D

Answer 10

What happened? Did you see it? It's sneaky. :-)

Answer 11

yes i see it...

Answer 12

n-1>3.419

Answer 13

bcoz the log is negative multiply with n

Answer 14

It didn't LOOK negative when it was written as a logarithm, did it? Good work.

Answer 15

yes

Answer 16

Thank you @tkhunny :)