7. Mr Jamil, a renowned engineer, designed a ball so that when it was dropped, it rose with each bounce
exactly one-half as high as it had fallen. The engineer dropped the ball from a 24-foot platform and
caught it after it had traveled 23.25 yards. How many times did the ball bounce?
(A) 7
(B) 11
(C) 6
(D) 5
(E) none
Answers
Answer:
6 answer h ball bounce krte hai
After 5 bounce engineer caught it
Step-by-step explanation:
Correction 23.25 is 23.5 yard
A ball dropped from 24 foot
Distance travelled = 24 foot before hitting
Then 24/2 = 12 foot bounce back & 12 feet Down to ground
Then 12/2 = 6 foot bounce back & 6 feet Down to ground
24 + 12 + 12 + 6 + 6 + 3 + 3 +.......
= 24 + 2 ( 12 + 6 + 3 +......................)
let say n bounces then
a = 12 r = 1/2
Sum = 12 ( 1 -(1/2)ⁿ)/(1 - 1/2) = 24 (1 - (1/2)ⁿ)
24 + 2 * 24 ( (1 - (1/2)ⁿ) is the distance
23.5 Yard = 23.5 * 3 = 70.5 feet
70.5 = 24 + 2 * 24 ( (1 - (1/2)ⁿ)
=> 46.5 = 48 - 48 (1/2)ⁿ
=> -1.5 = - 48(1/2)ⁿ
=> 2ⁿ = 32
=> n = 5
After 5 bounce engineer caught it
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