A physics book slides off a horizontal tabletop with a speed of 1.10m/s . It strikes the floor in 0.350s . Ignore air resistance.
The height of the tabletop above th floor is .600m.The horizontal distance from the edge of the table to the point where the book strikes the floor is .385m
Find the horizontal component of the book's velocity, just before the book reaches the floor.
Find the vertical component of the book's velocity just before the book reaches the floor.
The horizontal component of the book's velocity just before the book reaches the floor is 1.10 m/s.
The vertical component of the book's velocity just before the book reaches the floor is 4.22 m/s.
To find the horizontal component of the book's velocity just before it reaches the floor, we can use the equation:
v = d / t
where:
v = velocity (horizontal component)
d = horizontal distance
t = time
Given:
d = 0.385m
t = 0.350s
Substituting these values into the equation, we have:
v = 0.385m / 0.350s = 1.1m/s
Therefore, the horizontal component of the book's velocity just before it reaches the floor is 1.1m/s.
To find the vertical component of the book's velocity just before it reaches the floor, we can use the equation:
v = u + gt
where:
v = final velocity (vertical component) = ?
u = initial velocity (vertical component) = 0 (since the book starts from rest vertically)
g = acceleration due to gravity = 9.8m/s^2
t = time = 0.350s
Rearranging the equation to solve for v, we have:
v = u + gt
v = 0 + (9.8m/s^2)(0.350s)
v = 3.43m/s
Therefore, the vertical component of the book's velocity just before it reaches the floor is 3.43m/s.
To find the horizontal component of the book's velocity just before it reaches the floor, we need to calculate the horizontal distance traveled by the book in the given time.
The horizontal distance (d) can be calculated using the equation:
d = v * t
Where:
- v is the horizontal component of the book's velocity
- t is the time taken for the book to reach the floor
Given that the horizontal distance (d) is 0.385m and the time (t) is 0.350s, we can rearrange the equation to solve for v:
v = d / t
v = 0.385m / 0.350s
v ≈ 1.1m/s
Therefore, the horizontal component of the book's velocity just before it reaches the floor is approximately 1.1 m/s.
To find the vertical component of the book's velocity just before it reaches the floor, we can use the equation of motion:
h = (1/2) * g * t^2
Where:
- h is the vertical distance fallen (from the tabletop to the floor)
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time taken for the book to reach the floor
Given that the height (h) is 0.600m and the time (t) is 0.350s, we can rearrange the equation to solve for the vertical component of velocity:
h = (1/2) * g * t^2
0.600m = (1/2) * 9.8 m/s^2 * (0.350s)^2
Simplifying the equation:
0.600m = 0.5 * 9.8 m/s^2 * 0.1225s^2
0.600m = 0.59875 m
Therefore, the vertical component of the book's velocity just before it reaches the floor is approximately 0.599 m/s (upward direction).