Posted by Tina P on Tuesday, December 7, 2010 at 10:20am.
A ladder 10ft long rests against a vertical wall. If the bottom on the ladder slides away from the wall at 2 ft/s, how fast is the angle ladder makes with the ground changing when the bottom of the ladder is 5 ft from the wall.

Calculus 1  Reiny, Tuesday, December 7, 2010 at 10:28am
Let the foot be x ft from the wall, let the angle formed by the ladder at the ground be Ø
given: dx/dt = 2 ft/s
find: dØ/dt when x = 5
x/10 = cosØ
x = 10cosØ
dx/dt = 10sinØ dØ/dt
when x=5,
height^2 + 5^2 = 10^2
height = √75
2 = 10(√75/10) dØ/dt
dØ/dt =  2/√75 radians/second
= appr.  .23 rad/s

Calculus 1  Anonymous, Friday, October 23, 2015 at 5:16pm
100mph
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