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 is the angle 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.)

? rad/s

Community Answer

Step 1Given length of ladder =10ftx is the distance betwen the wall and ladderStep 2Let theta be the angle between the ladder & ground we have to find rate of charge of theta/_\ is right angle tianglecos theta=(x)/( 10)differentiate w.r.t ' t ' we get{:[-sin theta(d theta)/(dt)=(1)/(10)(dx)/(dt)],[(d theta)/(dt)=-(1)/(10 sin theta)(dx)/(dt)]:}from Deltasin theta=y//10Step 3Now we fi ... See the full answer