calculusssssssss

Question

A 14-foot ladder is leaning against a wall. If the top of the ladder slips down the wall at a rate of 2 ft/s., how fast will the end be moving away from the wall when the top is 6 ft. above the ground.

Answer 1

the bottom of the ladder is B feet away from the wall

use Pythagorean Theorem to calculate B = square root of (14^2 -6^2) =sqr(196+36) =sqf160 = 4sqr10

L= Ladder length, H= height of the top of the ladder, B = bottom of the ladder's length to the wall

L^2 = H^2 + B^2

take the derivative with respect to time

2LL' = 2HH' + 2BB'

divide by 2

LL' = HH' + BB' H'=2 B=4sqr10, L=14, L'=0, H=6

B'B =-HH'

B' = HH'/B = -6(2)/4sqr10 = -3/sqr10 =-3sqr10/10 = about -0.95 feet per second