Final answer:
The velocity of point B is 1.5 m/s to the left, and the acceleration of point B is 0.8 m/s² to the right, given that the ladder is rigid and moves translationally without rotation.
Step-by-step explanation:
To find the velocity and acceleration of point B when a 1 m ladder is sliding down a 30-degree slope, we need to apply the concepts of kinematics. Assuming point A is the top and point B is the bottom of the ladder, and given that the ladder is sliding to the left with a velocity of 1.5 m/s and an acceleration of 0.8 m/s² to the right, we can infer that the velocity of point B will also be 1.5 m/s to the left (since the ladder is rigid and of a fixed length, all points on the ladder will have the same velocity).
For the acceleration, we need to consider that if point A is accelerating to the right, the entire ladder, including point B, will experience the same acceleration. Thus, point B will also accelerate to the right with an acceleration of 0.8 m/s². This situation assumes there is no rotation and the ladder slides purely translationally down the slope.