please answer question 22
Answers
Answer:
Time of fall = (2 + √2) seconds = 3.414 seconds.
Explanation :
Time of journey (free fall) = t = n seconds
Height of free fall = H meters ;
Initial velocity = 0 ;
Acceleration due to gravity = g = 9.8 m/s²
Hn = (1/2) gt² = (1/2) gn² = distance travelled in n seconds
H(n-1) = (1/2) g (n - 1)² = distance travelled in n - 1 seconds
Distance travelled in the n th (last) second = h = Hn - H(n-1)
= (1/2)g {n² - (n - 1)²} = (1/2) g (2n - 1)
As per the question :
h = (1/2) Hn (1/2) g (2n - 1) = (1/4) g n²
=> 2n - 1 = n²/2
=> n² = 4n - 2
=> n² - 4n + 2 = 0
=> (n - 2)² - 2 = 0
=> (n - 2)² = 2
=> n - 2 = ± √2
=> n = 2 ± √2
=> n = (2 + √2) or (2 - √2)
For the values of n :-
n = 2 - √2, being less than 1, is rejected.
Time of journey = n = 2 + √2 seconds
Since, √2 = 1.414 (approx.)
Then,
Time of journey = n = 2 + 1.414 = 3.414 seconds (approx.)
Height of fall = (1/2) g (2 + √2)²
= (1/2)(9.8)(4 + 2 + 4√2)
= 9.8 × (3 + 2√2) meters
(Calculate by taking √2 = 1.414
By applying the values of √2, we get,
= 9.8 × (3 + 2 × 1.414) meters
= 57.1185858225 meters
Explanation:
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