a cherry explodes into three pieces of equal mass.one of the piece has an initial velocity of 10 m/sx.another piece has an initial velocity of 6.0 m/s x-3.0 m/s y.what is the velocityof the third piece
Conservation of momentum applies.
original momentum= final momentum
0= M*10 i + M*6i-M*3j + Mx i + My j
so to make the total s zero, Mx must =-16
and My must= + 3
To find the velocity of the third piece, we can use the principle of conservation of momentum. According to this principle, the total momentum before the explosion should be equal to the total momentum after the explosion.
Let's denote the mass of each piece as m, and we know that all three pieces have equal mass. Therefore, after the explosion, each piece will have a mass of m.
The total momentum before the explosion can be calculated by adding up the momenta of each piece, which is the product of its mass and velocity.
Momentum before = (mass of the first piece * velocity of the first piece) + (mass of the second piece * velocity of the second piece) + (mass of the third piece * velocity of the third piece)
Since the first piece has an initial velocity of 10 m/sx and the second piece has an initial velocity of 6.0 m/sx - 3.0 m/sy, we need to find the velocity of the third piece, which we will call V3.
Momentum before = (m * 10 m/sx) + (m * (6.0 m/sx - 3.0 m/sy)) + (m * V3)
After the explosion, the total momentum should remain the same. Since each piece has an equal mass of m, the total momentum after the explosion can be calculated as:
Momentum after = (m * V1) + (m * V2) + (m * V3)
where V1 is the velocity of the first piece, V2 is the velocity of the second piece, and V3 is the velocity of the third piece.
Since the total momentum before and after the explosion is the same, we can equate the two equations:
(m * 10 m/sx) + (m * (6.0 m/sx - 3.0 m/sy)) + (m * V3) = (m * V1) + (m * V2) + (m * V3)
Cancelling out the mass (m) on both sides, we get:
10 m/sx + (6.0 m/sx - 3.0 m/sy) + V3 = V1 + V2 + V3
Simplifying further, we find:
10 m/sx + 6.0 m/sx - 3.0 m/sy + V3 = V1 + V2 + V3
Combining like terms, we have:
16.0 m/sx - 3.0 m/sy + V3 = V1 + V2 + V3
Finally, rearranging the equation to isolate V3, we get:
V3 - V3 = (V1 + V2) - (16.0 m/sx - 3.0 m/sy)
V3 = V1 + V2 - 16.0 m/sx + 3.0 m/sy
Thus, the velocity of the third piece is equal to the velocity of the first piece plus the velocity of the second piece, minus 16.0 m/s in the x-direction, and plus 3.0 m/s in the y-direction.