a 5kg bomb exploded into two fragments. if one fragment with 3kg moves in a direction with 5m/s then what is the velocity of the send fragment of mass 2kg?

total momentum = 0

3*5 = 2*s
s = 7.5 m/s in opposite direction

To determine the velocity of the second fragment, we can make use of the law of conservation of momentum. According to this law, the total momentum before the explosion must be equal to the total momentum after the explosion.

The momentum of an object is given by the product of its mass and velocity. Therefore, the initial momentum before the explosion is:

Initial momentum = (Mass of Fragment 1 * Velocity of Fragment 1) + (Mass of Fragment 2 * Velocity of Fragment 2)

Given:
Mass of Fragment 1 = 3 kg
Velocity of Fragment 1 = 5 m/s
Mass of Fragment 2 = 2 kg (this is the second fragment)
Velocity of Fragment 2 = ??? (what we need to calculate)

Total mass before the explosion = Mass of Fragment 1 + Mass of Fragment 2 = 3 kg + 2 kg = 5 kg

Using the equation for conservation of momentum:

Initial momentum = Total mass before explosion * velocity of center of mass before explosion

The velocity of the center of mass before the explosion can be calculated using the masses and velocities of the fragments:

Velocity of center of mass before explosion = (Mass of Fragment 1 * Velocity of Fragment 1 + Mass of Fragment 2 * Velocity of Fragment 2) / (Total mass before explosion)

Substituting the given values:

(3 kg * 5 m/s + 2 kg * Velocity of Fragment 2) / 5 kg = 0

Simplifying the equation:

3 * 5 + 2 * Velocity of Fragment 2 = 0

15 + 2 * Velocity of Fragment 2 = 0

2 * Velocity of Fragment 2 = -15

Velocity of Fragment 2 = -15 / 2 = -7.5 m/s

Therefore, the velocity of the second fragment (with mass 2 kg) is -7.5 m/s. The negative sign indicates that its direction is opposite to that of the first fragment.