At a given instant the top b of the ladder has an...

At a given instant the top B of the ladder has an acceleration $a_B = 2.2 ft/s^2$ and a velocity of $v_B = 5.0 ft/s$, both acting downward. Determine the acceleration of the bottom A of the ladder. Express your answer to three significant figures and include the appropriate units. Determine the ladder's angular acceleration at this instant. Express your answer to three significant figures and include the appropriate units. Enter positive value if the angular acceleration is counterclockwise and negative value if the angular acceleration is clockwise.

Transcript

00:01 In this question, there's a letter that's making an angle that's placed against a wall and then making an angle 30 degrees from above the floor, horizontal floor.

00:13 And then at this instance, points b at the top of the ladder is moving down at 4 feet per second and acceleration 2 feet per second downward per second square downward.

00:25 Okay, and we need to determine the acceleration of point a and then and the lattice angular acceleration at this instance.

00:38 Okay, so we notes that va is to the left.

00:56 Okay, so likewise, the acceleration of point a will also be to the left.

01:04 So you can actually determine the instantaneous center of zero velocity which will be somewhere here.

01:15 This is the ic.

01:17 So we want this distance, which is 16 cosine degrees.

01:24 We can use this distance to determine omega of ab.

01:29 So omega ab is vb.

01:34 Vb divided by r i see to b.

01:39 Okay so this is 4 divided by 16 cosine 30 degrees.

01:51 Okay again it's going to move clockwise.

01:57 So this is going to be 1 over 2 root 3.

02:07 Okay this is equal to 0 .289.

02:11 Radiance per second okay then we can use the relative acceleration equation a a is a b plus alpha a b cross r b relative to a minus omega a b square r b relative to a okay so a b is so this is minus a a a a in the i direction ab is minus 2j, alpha ab is minus alpha ab, is minus alpha ab, k, cross rb relative to a will be minus 16, cosine 30 degrees i, plus sine 30 degrees j...

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