# Question A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast (in rad/s) is the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.) Wall 10 Ground - 1/10 Xrad/s

1D6ZGT The Asker · Calculus

Transcribed Image Text: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast (in rad/s) is the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.) Wall 10 Ground - 1/10 Xrad/s
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Transcribed Image Text: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 0.8 ft/s, how fast (in rad/s) is the angle (in radians) between the ladder and the ground changing when the bottom of the ladder is 8 ft from the wall? (That is, find the angle's rate of change when the bottom of the ladder is 8 ft from the wall.) Wall 10 Ground - 1/10 Xrad/s
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SDBCVP

Longrightarrow^(" Aus "rarr) Let y be the height of ladder and x be the distance from wals.{:[" length of ladder "=10ft],[(dx)/(dt)=0.8ft//s]:}Now frem /_\ABC{:[cos theta=(x)/( 10)],[=>x=10 cos theta],[dif ^(n)w*r*" to "(t)],[(dx)/(dt)=10(d)/(dt)cos theta],[=>(dx)/(dt)=-10 sin theta*(d theta)/(dt)],[N=omega EBD],[=>cos theta=(8)/(10)=>cos theta ... See the full answer