A physics book slides off a horizontal table top with a speed of 1.30 m/s . It strikes the floor after a time of 0.380s . Ignore air resistance.
Find the height of the table top above the floor.
Find the horizontal distance from the edge of the table to the point where the book strikes the floor
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.
Find the magnitude of the book's velocity just before the book reaches the floor
Find the direction of the book's velocity just before the book reaches the floor.
Express your answer as an angle measured below the horizontal
a gun is adjusted so that the barrel of the jun is in line with and pointed at the center of a target. the distance from the gun to target is 121.0m. when the gun is fired the bullet hits 10.00cm below the center of the target. find the muzzle velocity of gun?
To solve this problem, we can use the equations of motion to find the values required. Here are the step-by-step solutions for each part:
1. Finding the height of the table top above the floor:
We can use the equation of motion for free fall to find the height.
Height = 1/2 * acceleration * time^2
Since the book is falling under gravity, the acceleration is equal to the acceleration due to gravity, denoted as "g". So, we have:
Height = 1/2 * g * (time)^2
Substituting the known values:
Height = 1/2 * 9.8 m/s^2 * (0.380 s)^2
Height ≈ 0.698 m
Therefore, the height of the table top above the floor is approximately 0.698 meters.
2. Finding the horizontal distance from the edge of the table to the point where the book strikes the floor:
The horizontal distance travelled by the book can be calculated using the equation:
Distance = initial velocity * time
Since the book slides off a horizontal table top, its initial horizontal velocity is equal to the velocity at which it slides off, which is 1.30 m/s. Therefore, we have:
Distance = 1.30 m/s * 0.380 s
Distance ≈ 0.494 m
Hence, the horizontal distance from the edge of the table to the point where the book strikes the floor is approximately 0.494 meters.
3. Finding the horizontal component of the book's velocity just before it reaches the floor:
The horizontal component of velocity remains constant throughout the motion because there is no horizontal force acting on the book. Therefore, the horizontal component of velocity just before it reaches the floor is equal to the initial horizontal velocity, which is 1.30 m/s.
Hence, the horizontal component of the book's velocity just before it reaches the floor is 1.30 m/s.
4. Finding the vertical component of the book's velocity just before it reaches the floor:
The vertical component of velocity can be found using the equation:
Vertical Velocity = Initial Vertical Velocity + (acceleration * time)
The initial vertical velocity is 0 m/s as the book starts from rest in the vertical direction. The acceleration due to gravity is acting in the downward direction, so we take it as -9.8 m/s^2 (negative because it is acting opposite to the positive direction). The time is given as 0.380 seconds. Using the formula:
Vertical Velocity = 0 m/s + (-9.8 m/s^2) * (0.380 s)
Vertical Velocity ≈ -3.724 m/s
Therefore, the vertical component of the book's velocity just before it reaches the floor is approximately -3.724 m/s.
5. Finding the magnitude of the book's velocity just before it reaches the floor:
The magnitude of velocity can be found using the Pythagorean theorem, which states that for a right triangle:
(Velocity)^2 = (Horizontal Velocity)^2 + (Vertical Velocity)^2
Plugging in the known values:
(Velocity)^2 = (1.30 m/s)^2 + (-3.724 m/s)^2
(Velocity)^2 ≈ 13.69 m^2/s^2
Velocity ≈ √13.69 m/s
Velocity ≈ 3.698 m/s
So, the magnitude of the book's velocity just before it reaches the floor is approximately 3.698 m/s.
6. Finding the direction of the book's velocity just before it reaches the floor:
The direction of the book's velocity can be determined using trigonometry. We can find the angle below the horizontal using the equation:
Angle = arctan(Vertical Velocity / Horizontal Velocity)
Plugging in the known values:
Angle = arctan((-3.724 m/s) / (1.30 m/s))
Angle ≈ -70.039 degrees
Therefore, the direction of the book's velocity just before it reaches the floor is approximately 70.039 degrees below the horizontal.