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A ladder of length b rests against a vertical wall (see figure). The base of the ladder is pulled away with a constant speed vo. a. Show that the midpoint M of the ladder describes the arc of a circle of radius b/2 with the center at 0. b. Find the velocity of the midpoint M at the moment where the base of the ladder is at a distance a < b from the wall.

A ladder of length b rests against a vertical wall (see figure). The base of the ladder is pulled away with a constant speed vo. a. Show that the midpoint M of the ladder describes the arc of a circle of radius b/2 with the center at 0. b. Find the velocity of the midpoint M at the moment where the base of the ladder is at a distance a < b from the wall.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. A ladder of length b rests against a vertical wall (see figure). The base of the ladder is pulled away with a constant speed vo. a. Show that the midpoint M of the ladder describes the arc of a circle of radius b/2 with the center at 0. b. Find the velocity of the midpoint M at the moment where the base of the ladder is at a distance a < b from the wall. Wall 2. 3. 4. Given two matrices, determine AB and BÃ. Is AB = BĂ? 7. The position of a particle is given by M = Floor 7= A(etê + e-tê₂) where a is a constant. Find the velocity and sketch the trajectory. (Hint: In sketching the motion of a particle, it is usually helpful to look at limiting cases as t→0 and as t → 00.) The position of a particle at any time t is given by x = a, y = bt², where a and bare constants. Find the rectangular and polar components of its velocity and acceleration (a) at any time t, (b) when a = 12 cm, b = 1 cm/s², and when t = 3 s. 5. A particle moves along a space curve C with a vector is given by 7(t) = 3 cos 2t ê₁ + 3 sin 2t ê₂ + (8t - 4) 3 a. Find a unit tangent vector to the curve C. b. Show that = v 6. A particle moves at a constant acceleration along the curve x₂ = x₁/100 from point A to point B. The velocity of the particle at A is 10 m/s, and 10 s later, at point B it is traveling at 50 m/s. Determine the total acceleration of the particle at point B. Show that finite rotation is not a vector quantity.
Transcribed Image Text:1. A ladder of length b rests against a vertical wall (see figure). The base of the ladder is pulled away with a constant speed vo. a. Show that the midpoint M of the ladder describes the arc of a circle of radius b/2 with the center at 0. b. Find the velocity of the midpoint M at the moment where the base of the ladder is at a distance a < b from the wall. Wall 2. 3. 4. Given two matrices, determine AB and BÃ. Is AB = BĂ? 7. The position of a particle is given by M = Floor 7= A(etê + e-tê₂) where a is a constant. Find the velocity and sketch the trajectory. (Hint: In sketching the motion of a particle, it is usually helpful to look at limiting cases as t→0 and as t → 00.) The position of a particle at any time t is given by x = a, y = bt², where a and bare constants. Find the rectangular and polar components of its velocity and acceleration (a) at any time t, (b) when a = 12 cm, b = 1 cm/s², and when t = 3 s. 5. A particle moves along a space curve C with a vector is given by 7(t) = 3 cos 2t ê₁ + 3 sin 2t ê₂ + (8t - 4) 3 a. Find a unit tangent vector to the curve C. b. Show that = v 6. A particle moves at a constant acceleration along the curve x₂ = x₁/100 from point A to point B. The velocity of the particle at A is 10 m/s, and 10 s later, at point B it is traveling at 50 m/s. Determine the total acceleration of the particle at point B. Show that finite rotation is not a vector quantity.
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