Calculus 1
posted by Tina P .
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.

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 
100mph
Respond to this Question
Similar Questions

Math
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 1.2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 8 ft … 
Math
a ladder 10 ft long rests against a vertical wal. if the bottom of the ladder slides away from the wall at a rate of 0.7 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 6 ft fro the wall? 
Calculus Ladder Problem
A ladder 20 ft long rests against a vertical wall. Let \theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from … 
calculus
A ladder 14 ft long rests against a vertical wall. Let \theta be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from … 
Calculus
A 5m long ladder rests on a vertical wall. if the bottom of the ladder slides away from the wall at 1m/s, how fast is the angle between the lader and the ground changing when the bottom of the ladder is 3m from the wall? 
calculus
A ladder 10 ft long rests against a vertical wall. let θ be the angle between the top of the ladder and the wall and let x be the distance from the bottom of the ladder to the wall. If the bottom of the ladder slides away from … 
Related Rates
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 2 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the ladder is 5 ft from … 
Calculus
A ladder 10 ft 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
Related Rates: 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 0.9 ft/s, how fast is the angle between the ladder and the ground changing when the bottom of the … 
Calculus
A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from the wall at a rate of 1 ft. per second,how fast is the angle between the ladder and the ground changing when the bottom of the ladder is …