Three bullets are fired simultaneously by three guns aimed toward the center of a circle where the bullets mash into a stationary lump. The angle between the guns is 120°. Two of the bullets have a mass of 9.30 10-3 kg and are fired with a speed of 440 m/s. The third bullet is fired with a speed of 650 m/s and we wish to determine the mass of this bullet.

Question

Three bullets are fired simultaneously by three guns aimed toward the center of a circle where the bullets mash into a stationary lump. The angle between the guns is 120°. Two of the bullets have a mass of 9.30 10-3 kg and are fired with a speed of 440 m/s. The third bullet is fired with a speed of 650 m/s and we wish to determine the mass of this bullet.

Answer 1

To determine the mass of the third bullet, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision must be equal to the total momentum after the collision, assuming no external forces are acting on the system.

Let's denote the mass of the third bullet as m3 and its velocity as v3. The mass of the first two bullets is given as 9.30 x 10^-3 kg and their velocity is given as 440 m/s.

Before the collision, the total momentum of the system is the vector sum of the individual momenta of each bullet. Since the bullets are fired simultaneously and aimed toward the center of the circle, we can assume that their velocities are along a straight line. Thus, the total momentum before the collision can be represented as:

P_initial = m1 * v1 + m2 * v2 + m3 * v3

where m1 = m2 = 9.30 x 10^-3 kg, v1 = v2 = 440 m/s, and v3 is the velocity of the third bullet.

We know that the angle between the guns is 120°. Since the bullets are fired simultaneously, they will reach the center of the circle at the same time. Therefore, the angle between the velocities v1 and v2 is also 120°.

Using the law of cosines, we can determine the magnitude of the velocity of the third bullet:

v3^2 = v1^2 + v2^2 - 2 * v1 * v2 * cos(120°)
v3^2 = (440 m/s)^2 + (440 m/s)^2 - 2 * (440 m/s) * (440 m/s) * cos(120°)

Now, we can substitute this expression for v3^2 back into the equation for the total momentum:

P_initial = m1 * v1 + m2 * v2 + m3 * (v3^2)^0.5

Since we're solving for m3, we rearrange the equation to solve for m3:

m3 = (P_initial - m1 * v1 - m2 * v2) / (v3^2)^0.5

Substituting the given values into this equation, we can find the mass of the third bullet.

Answer 2

Unless you tell us something about the velocity of the resulting 3-bullet lump, there's no way to tell anything about its mass.

Also, are the three gun muzzles arranged in a circle parallel to the plane of the target?