very urgent 聽日測驗la!

2006-10-27 8:44 am

1..An elastic ball is dropped from a height of h m(metre). It rebounds to a height of (3/5)h and continues to fall and rebound, rising to a height of (3/5)^2 h and so on . If h is 100 m , find:
a) the height reached after the 6 th rebound;
b) how many more times must the ball rebound before its height of rebound becomes less than 1 m .
c) the total distances, to the nearest m , the ball has travelled before it comes to rest;

回答 (1)

用戶53370

2006-10-27 9:15 am

✔ 最佳答案

1. a) height = 100 * (3/5)^6 = 4.6656m

b) 4.6656 * (3/5) ^ n < 1
n = 4

*** You can take log to find n where n is an integer

c) total distances = 100 + 100* (3/5) * 2 + 2* 100* (3/5) ^ 2 + 2 * 100 * (3/5) ^ 3 + ... + 2 * 100 * (3/5) ^ n where n is infinity

= 100 + 200 * [3/5 + (3/5)^2 + (3/5)^3 + ... + (3/5)^n + ...]
= 100 + 200 * (3/5) /(1-3/5)
= 400

*** this is sum to infinity problem

2. Let t be the number of seconds after they travel

(t) (t+1)/2 + 5t = 261
t^2 + 11t - 522 = 0
(t+29) (t-18) = 0
t = 18 (because t > 0)

They meet at 18 seconds and at the point of 90m (because Y travels 5m per second).

*** this is sum of arimetic progression

2006-10-27 01:16:26 補充：
Sorry, a) should be 466.56m

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