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.
1.1m/s and-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 displacement of the book.
Given:
Initial horizontal velocity (u) = 1.10 m/s
Time of flight (t) = 0.350 s
Horizontal distance (s) = 0.385 m
We can use the equation: s = ut
Substituting the given values:
0.385 = 1.10 × 0.350
Dividing both sides of the equation by 0.350:
0.385/0.350 = 1.10
Therefore, the horizontal component of the book's velocity just before it reaches the floor is 1.10 m/s.
To find the vertical component of the book's velocity just before it reaches the floor, we can use the equation for free fall motion:
Height (h) = 0.600 m (height of tabletop above the floor)
Acceleration due to gravity (g) = 9.8 m/s^2 (approximate value on Earth)
We can use the equation for vertical displacement:
h = ut + (1/2)gt^2
Since the book falls vertically, the initial vertical velocity (u) is zero:
0.600 = 0 × t + (1/2) × 9.8 × t^2
Simplifying the equation:
0.600 = 4.9t^2
Dividing both sides by 4.9:
0.600/4.9 = t^2
Taking the square root of both sides:
√(0.600/4.9) = t
Therefore, the time of flight (t) is approximately 0.139 seconds.
Now, we can calculate the vertical component of the book's velocity just before it reaches the floor using the equation:
u = gt
Substituting the values:
u = 9.8 × 0.139
Calculating:
u ≈ 1.36 m/s
Therefore, the vertical component of the book's velocity just before it reaches the floor is approximately 1.36 m/s.
To find the horizontal component of the book's velocity just before it reaches the floor, we need to calculate the horizontal distance covered by the book in the given time.
First, let's calculate the horizontal distance covered by the book. We are given that the book struck the floor in 0.350 seconds, and the horizontal distance from the edge of the table to the point where the book strikes the floor is 0.385 meters. So, the horizontal velocity of the book can be calculated using the formula:
horizontal velocity = horizontal distance / time
horizontal velocity = 0.385 m / 0.350 s
Next, we calculate the horizontal component of the book's velocity just before it reaches the floor. Since there is no horizontal acceleration (ignoring air resistance), the horizontal component of the book's velocity remains constant throughout its motion. Therefore, the horizontal component of the book's velocity just before it reaches the floor is the same as its initial horizontal velocity, which is the value we calculated previously.
In this case, the horizontal component of the book's velocity just before it reaches the floor is equal to 1.1 m/s.
Now, let's find the vertical component of the book's velocity just before it reaches the floor. We can use the kinematic equation for vertical motion:
vertical displacement = (initial vertical velocity * time) + (0.5 * acceleration * time^2)
The initial vertical velocity is 0 since the book is initially at rest in the vertical direction. The vertical displacement is the height of the tabletop above the floor, which is given as 0.6 meters. The time is 0.350 seconds.
Using the equation, we can rearrange it to solve for the vertical component of the book's velocity:
vertical component of velocity = (vertical displacement - 0.5 * acceleration * time^2) / time
vertical component of velocity = (0.6 m - 0.5 * 9.8 m/s^2 * (0.35 s)^2) / 0.35 s
Using this equation, you can calculate the vertical component of the book's velocity just before it reaches the floor.
For Vx which is the horizontal velocity component:
Vx=d/t
Vx=.385m/.350s= 1.10m/s
For Vy the vertical velocity component:
Vy=gt g=-9.8m/s2 for gravity
Vy=(-9.8m/s2)(0.350s)= -3.43m/s