Question

In: Math

A 10ft long ladder that is leaning against a wall is being pushed. The top of...

A 10ft long ladder that is leaning against a wall is being pushed. The top of the ladder moves upward along the wall at a speed of 1.5 ft/sec. At what rate is the bottom of the ladder sliding toward the wall when the base is 6 feet from the wall? Is your answer positive or negative? Explain why the answer you got makes sense. Draw a picture of the situation and clearly label your variables.

Solutions

Expert Solution

we have

we know that,

....................... paythagoras theorm

put x =8, l=10,

now,

here l = 10 (constant)

here negative sign indicate the distance is decreases.

the rate of bottom of the ladder sliding toward the wall when the base is 6 feet from the wall is 2 ft/sec


Related Solutions

A ladder 25 feet long is leaning against the wall of a house. The base of...
A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 2 feet per second. How fast is the top of the ladder moving down the wall when the base is 15 feet from the wall? Consider the triangle formed by the side of the house, the ladder, and the ground. Find the rate at which the area of the triangle is changing...
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 uniform 6.0 kg ladder is leaning against a frictionless vertical wall, with which it makes...
A uniform 6.0 kg ladder is leaning against a frictionless vertical wall, with which it makes a 15 ?angle. The coefficient of friction between ladder and ground is 0.26. Can a 58 kg person climb to the top of the ladder without it slipping? If so, how massive a person would make the ladder slip?
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.)
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 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
a 5.5m ladder is leaning against a house when its base starts to slide away. By...
a 5.5m ladder is leaning against a house when its base starts to slide away. By the time the base is 4.44.4 m from the​ house, the base is moving away at the rate of 9.99.9 ​m/s. a. What is the rate of change of the height of the top of the​ ladder? b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​ then? thetaθ x(t)y(t)05.5 m ladderxy c. At what rate...
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.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT