A ladder 20 ft long has one end on the ground and the other end in contact with a vertical wall. The lower end slips along the ground. If the lower end of the ladder is 16 ft away from the wall, upper end is moving lambda times as fast as the lower end, then lambda is A. 1/3 B. 2/3 C. 4/3 D. 5/3

Rylee Friedman

Rylee Friedman

Answered question

2023-01-11

A ladder 20 ft long has one end on the ground and the other end in contact with a vertical wall. The lower end slips along the ground. If the lower end of the ladder is 16 ft away from the wall, upper end is moving λ times as fast as the lower end, then λ is
A. 1 3
B. 2 3
C. 4 3
D. 5 3

Answer & Explanation

tappahtappahwf6

tappahtappahwf6

Beginner2023-01-12Added 11 answers

Let OC be the wall. Let AB be the position of the ladder at any time t such that OA = x and OB = y. Length of the ladder AB = 20 ft. In ΔAOB,
x 2 + y 2 = ( 20 ) 2
2 x d x d t + 2 y d y d t = 0 d y d t = x y . d x d t = x 400 x 2 . d x d t = 16 400 ( 16 ) 2 . d x d t = 4 3 d x d t
–ve sign indicates, that when x increases with time, y decreases.
In light of this, the upper end is moving 4/3 as quickly as the lower end.

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