The speed of a moving bullet can be determined by allowing the bullet to pass through
two rotating paper disks mounted a distance
100 cm apart on the same axle. From the
angular displacement 22.9
◦
of the two bullet holes in the disks and the rotational speed
707 rev/min of the disks, we can determine
the speed of the bullet.
Assuming a finite speed of the bullet, yet fast enough that the disc cannot make a full revolution while the bullet flies the 100cm, then things are ok.
707rev/min = 707*360°/min = 707*360°/60s = 4242°/s
Since it only rotated 22.9°, we can assume the bullet took 22.9/4242 = 0.00539s to travel 100cm
Speed = 100cm/.00539s = 18552cm/s, or 185.52m/s
To determine the speed of a moving bullet using the given information, you can follow these steps:
1. Convert the angular displacement from degrees to radians: The angular displacement given in degrees (22.9°) needs to be converted to radians. To convert, use the formula: radians = degrees × (π/180). So, the angular displacement in radians would be: radians = 22.9 × (π/180).
2. Calculate the linear distance traveled by the bullet: The linear distance is the arc length between the two bullet holes on the rotating disks. To find the linear distance, you need to know the radius of the disks. Assuming the radius of the disks is "r," the formula for arc length is: arc length = radius × angular displacement. So, the linear distance traveled by the bullet would be: distance = r × radians.
3. Convert the rotational speed from revolutions per minute (rev/min) to radians per second (rad/s): The rotational speed of the disks given in rev/min needs to be converted to rad/s. To convert, use the formula: radians per second = revolutions per minute × (2π/60). So, the rotational speed in rad/s would be: speed = 707 × (2π/60).
4. Calculate the time for the bullet to travel the distance between the two disks: The time taken by the bullet to travel the distance between the two disks can be found using the formula: time = distance / speed. Substitute the values of distance and speed determined in steps 2 and 3 to calculate the time.
5. Determine the speed of the bullet: Finally, you can find the speed of the bullet by dividing the linear distance traveled (step 2) by the time taken (step 4). This will give you the speed of the bullet in cm/s.
By following these steps, you can determine the speed of the bullet using the given angular displacement and rotational speed of the disks.