Final answer:
The height of the table top above the floor is approximately 0.398 meters. The horizontal distance from the edge of the table to the point where the book strikes the floor is approximately 0.779 meters. The magnitude of the horizontal component of the book's velocity just before it reaches the floor is 1.90 m/s.
Step-by-step explanation:
Given the initial speed of the book sliding off the table (v₀ = 1.90 m/s) and the time it takes to reach the floor (t = 0.410 s), we can calculate the height of the table top using the equation:
h = v₀t + (1/2)gt²
where g is the acceleration due to gravity (approximately 9.8 m/s²). Substituting the given values into the equation, we get:
h = (1.90 m/s)(0.410 s) + (1/2)(9.8 m/s²)(0.410 s)² = 0.398 m
Therefore, the height of the table top above the floor is approximately 0.398 meters.
To find the horizontal distance from the edge of the table to the point where the book strikes the floor, we can use the equation:
d = v₀t
Substituting the given values, we get:
d = (1.90 m/s)(0.410 s) = 0.779 meters
Therefore, the horizontal distance from the edge of the table to the point where the book strikes the floor is approximately 0.779 meters.
Finally, to find the magnitude of the horizontal component of the book's velocity just before it reaches the floor, we can use the equation:
vₓ = d / t
Substituting the given values, we get:
vₓ = (0.779 meters) / (0.410 s) = 1.90 m/s
Therefore, the magnitude of the horizontal component of the book's velocity just before it reaches the floor is 1.90 m/s.