Question

The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance

87 cm apart on the same axle. From the
angular displacement of 21.6◦
of the two bullet holes in the disks and the rotational speed
537 rev/min of the disks, we can determine
the speed of the bullet.
What is the speed of the bullet?
Answer in units of m/s.

Answer 1

The speed of the bullet is calculated by first converting the angular displacement to radians and finding the time it took to travel between the two rotating disks. Then, using the distance between the disks, the speed is determined to be 129.85 m/s.

Step-by-step explanation:

The speed of the bullet can be calculated using the angular displacement of the bullet holes in the rotating disks and the rotational speed of the disks. Given an angular displacement of 21.6 degrees and a rotational speed of 537 revolutions per minute (rev/min), we first convert the angular displacement to radians (1 degree = 0.0174533 radians) and then calculate the time the bullet took to travel between the two disks:

21.6 degrees * 0.0174533 rad/degree = 0.376991 rad

The disks rotate at 537 rev/min, which we convert to radians per second:

537 rev/min * (1 min/60 s) * (2π rad/1 rev) = 56.27 rad/s

Now, we can find the time it took for the bullet to travel between the disks:

Time = Angular displacement / Angular velocity

Time = 0.376991 rad / 56.27 rad/s = 0.0067 s

Finally, using the distance between the disks, we can calculate the speed of the bullet:

Speed = Distance / Time

Speed = 0.87 m / 0.0067 s = 129.85 m/s

Answer 2

130 m/s

Step-by-step explanation:

First use the angular displacement to find the time.

Δθ = ω t

21.6° × (1 rev / 360°) = 537 rev/min × (1 min / 60 s) t

t = 0.0067 s

Now use the distance to find the speed.

v = Δx / t

v = 0.87 m / 0.0067 s

v = 130 m/s