Question

In: Math

A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder...

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 1.4 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.)

Solutions

Expert Solution

--------(1)

Differentiating with t

(Because )

(putting the value of from equation (1))

(L=10 ft ; x=8 ft ; dx/dt=1.4 ft/s


Related Solutions

A 15 ft ladder leans against a wall. The bottom of the ladder is 3 ft...
A 15 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and slides away from the wall at a rate of 1 ft/sec. Find the velocity of the top of the ladder at time t=3. The velocity of the ladder at time t=3 is --ft/sec
1. A 20 foot ladder leans against a vertical wall. The bottom of the ladder slides...
1. A 20 foot ladder leans against a vertical wall. The bottom of the ladder slides away from the wall at 2 ft/sec. a. How fast is the top of the ladder sliding down the wall when the top of the ladder is 12 feet from the ground? b. Interpret the meaning of the sign.
A ladder having a uniform density and a mass m rests against a frictionless vertical wall,...
A ladder having a uniform density and a mass m rests against a frictionless vertical wall, making angle 48.0° with the horizontal. The lower end rests on a flat surface where the coefficient of static friction is µs = 0.370. A window cleaner with mass M = 2m attempts to climb the ladder. Given a ladder length of L, what fraction of the length of the ladder (x / L) will the worker have reached when the ladder begins to...
A uniform ladder 5.30  m long rests against a frictionless, vertical wall with its lower end 3.10  m...
A uniform ladder 5.30  m long rests against a frictionless, vertical wall with its lower end 3.10  m from the wall. The ladder weighs 161  N . The coefficient of static friction between the foot of the ladder and the ground is 0.390. A painter weighing 741  N climbs slowly up the ladder. a)What is the actual size of the frictional force when the painter has climbed 1.0197  m along the ladder? b)How far along the ladder can the painter climb before the ladder starts...
A uniform ladder 5.30  m long rests against a frictionless, vertical wall with its lower end 3.10  m...
A uniform ladder 5.30  m long rests against a frictionless, vertical wall with its lower end 3.10  m from the wall. The ladder weighs 157  N . The coefficient of static friction between the foot of the ladder and the ground is 0.430. A painter weighing 739  N climbs slowly up the ladder. How far along the ladder can the painter climb before the ladder starts to slip?
A ladder is leaning against a vertical wall, and both ends of the ladder are at...
A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is μ1 = 0.205 and the coefficient of friction between the ladder and the wall is μ2 = 0.153. Determine the maximum angle with the vertical the ladder can make without falling on the ground.
A ladder is leaning against a vertical wall, and both ends of the ladder are at...
A ladder is leaning against a vertical wall, and both ends of the ladder are at the point of slipping. The coefficient of friction between the ladder and the horizontal surface is ?1 = 0.215 and the coefficient of friction between the ladder and the wall is ?2 = 0.203. Determine the maximum angle with the vertical the ladder can make without falling on the ground.
A 5m ladder leans against a wall. The bottom of the ladder is 2m from the...
A 5m ladder leans against a wall. The bottom of the ladder is 2m from the wall at time ?=0 sec and slides away from the wall at a rate of 0.8m/s. Find the velocity of the top of the ladder at time ?=2 (take the direction upwards as positive). (Use decimal notation. Give your answer to three decimal places.)
A 10.0kg uniform ladder that is 2.50m long is placed against a smooth (frictionless) vertical wall...
A 10.0kg uniform ladder that is 2.50m long is placed against a smooth (frictionless) vertical wall and reaches to a height of 2.10m. The angle between the floor and the ladder is 60°. An 80.0kg bucket of concrete is suspended from the top rung of the ladder, right next to the wall. a) Draw a free-body diagram of the ladder. b) What is the magnitude of the friction force, that the floor exerts on the ladder? c) What is the...
A uniform ladder rests against a frictionless wall at an angle of θ = 48.0° with...
A uniform ladder rests against a frictionless wall at an angle of θ = 48.0° with respect to the ground. If the weight of the ladder is WL = 250 N, the length is L = 9.0 m, and the coefficient of static friction between the ladder and the ground is μs = 0.60, determine the distance a man with a weight of WM = 900 N can climb along the ladder before the ladder begins to slip m?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT