The top of a 20-foot ladder leans against a wall, and the bottom of the ladder s

Question

The top of a 20-foot ladder leans against a wall, and the bottom of the ladder slides away from the wall at a rate of 5 ft/sec. Find the velocity of the top of the ladder at time t = 1 sec if the bottom of the ladder is 7 feet away from the wall at time t = 0.

Explanation / Answer

let h = length of ladder ; a = distance from bottom of ladder to the wall ; b = distance of the top from the floor ................... so at t =0 a= 7ft ...........we have h^2 = a^2 + b^2 ...........at t=0 we have 20^2 = 7^2 + b^2 ==> b = sqrt (351)ft ...................at t= 1 sec bottom moved 5 ft from original place so .....a = 7+5 =12 ft ............now 20^2 = 12^2 + b'^2 ..........==> b' = 16 ft ............so in 1 sec of time the top of the ladder has traveled (sqrt(351) - 16 ) ft ..........so the velocity of top of the ladder = (sqrt(351) - 16 )ft / 1sec = 2.735 ft / sec downwards

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