A 16 kg object with a velocity 7.5 m/s explodes into two equal fragments. One flies off with a velocity 2.5i -2.5j m/s.
What is the velocity of the other fragment in vector notation?
dis is rong
Momentum is conserved. With two masses, the second mass velocity must be the negative of the first.
V=-(2.5i-2.5j)
so the 7.5 is irrelevant ?
To find the velocity of the other fragment with vector notation, we can use the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the explosion is equal to the total momentum after the explosion.
The momentum of an object is given by its mass multiplied by its velocity. Therefore, the total momentum before the explosion is equal to the sum of the momenta of the two fragments.
Before the explosion:
Total momentum = mass of object * velocity of object
After the explosion:
Total momentum = (mass of one fragment * velocity of one fragment) + (mass of the other fragment * velocity of the other fragment)
Given:
Mass of object = 16 kg
Velocity of object = 7.5 m/s
Velocity of one fragment = 2.5i - 2.5j m/s
We need to find the velocity of the other fragment.
Let's assume the velocity of the other fragment is Vi.
Applying the principle of conservation of momentum, we can write the equation as:
16 kg * 7.5 m/s = 16/2 kg * (2.5i - 2.5j) + 16/2 kg * Vi
Simplifying the equation:
120 kg*m/s = 8 kg * (2.5i - 2.5j) + 8 kg * Vi
Now we can solve for Vi.
120 kg*m/s = (20i - 20j) + 8 kg * Vi
Since the velocities are in vector notation, we can separate the equation into its components:
For the x-component:
0 = 20 + 8 Vi (comparing the x-components)
For the y-component:
0 = -20 + 8 Vi (comparing the y-components)
Solving for Vi by substituting these values:
0 = 20 + 8 Vi
Vi = -20/8
Vi = -2.5 m/s
Therefore, the velocity of the other fragment in vector notation is -2.5 m/s in the opposite direction (i.e., -2.5i + 2.5j m/s).