1.0kg bomb explodes into three pieces, A, B, and C

A ( 0.3kg) travel along the positive x-axis by 0.3km/s
B (0.5kg) travel along the negative y-axis by 04km/s
What is the velocity of C?

conserve momentum.

0.3*0.3<1,0> + 0.5*0.4<0,-1> + 0.2*<x,y> = <0,0>
<0.09,0> + <0,-0.20> + 0.2<x,y> = <0.09,-0.20> + <0.2x+0.2y> = <0,0>

.09+.2x = 0
x = -.45

-.20+0.2y = 0
y = 1.00

so now just find the magnitude and direction of <-0.45,1.00>

momentum is conserved , so C's momentum cancels A's and B's

mass C = 1.0 kg - (0.3 kg + 0.5 kg) = 0.2 kg

the opposite of A momentum is ... .09 kg⋅m/s along negative x-axis

the opposite of B momentum is ... 0.2 kg⋅m/s along positive y-axis

C momentum is the resultant (vector addition) of the two opposites
... velocity of C is the momentum divided by the mass

Would C velocity be 2.9m/s toward North-West?

To find the velocity of piece C, we need to use the law of conservation of momentum. According to this law, the total momentum before the explosion is equal to the total momentum after the explosion.

The momentum of an object is given by the product of its mass and velocity: momentum = mass * velocity.

Let's calculate the momenta of pieces A and B:

Momentum of A = mass of A * velocity of A
= 0.3 kg * 0.3 km/s
= 0.09 kg·km/s

Momentum of B = mass of B * velocity of B
= 0.5 kg * (-0.4 km/s)
= -0.2 kg·km/s

Now, since the total momentum before the explosion is equal to the total momentum after the explosion, we can write the equation:

total momentum before = total momentum after

The total momentum before the explosion is zero because the bomb is not moving initially.

0 = momentum of A + momentum of B + momentum of C

We want to find the velocity of piece C, so let's denote it as vC.

0 = 0.09 kg·km/s + (-0.2 kg·km/s) + mass of C * vC

Since the total mass of the bomb is 1 kg and we know the masses of pieces A and B, we can calculate the mass of C:

mass of C = total mass - mass of A - mass of B
= 1 kg - 0.3 kg - 0.5 kg
= 0.2 kg

Now we can rearrange the equation to solve for the velocity of C:

mass of C * vC = -(0.09 kg·km/s + 0.2 kg·km/s)
vC = -(0.29 kg·km/s) / 0.2 kg
vC = -1.45 km/s

Therefore, the velocity of piece C is -1.45 km/s in the negative direction.