A 6.2 kg model rocket is traveling horizontally and due south with a speed of 20.3 m/s when it explodes into two pieces. The velocity of one piece, with a mass of 1.6 kg, is

v1 = (-12 m/s)i + (30 m/s)j + (15 m/s)k,

with i pointing due east, j pointing due north, and k pointing vertically upward.

(a) What is the velocity of the other piece, in unit-vector notation?
m/s i
m/s j
m/s k
(b) What is the kinetic energy of the other piece?
J
(c) How much kinetic energy is produced by the explosion?
J

can someone please answer this lmao I need c

To solve this problem, 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.

Before the explosion, the total momentum of the system is given by the product of the total mass and the initial velocity:

Total Momentum before explosion = (6.2 kg + 1.6 kg) * (20.3 m/s)

Now, let's calculate the x, y, and z components of the total initial momentum.

x-component: m1 * v1_x + m2 * v2_x
y-component: m1 * v1_y + m2 * v2_y
z-component: m1 * v1_z + m2 * v2_z

We know the x, y, and z components of v1, so we can substitute those values into the equation above.

Now, after the explosion, the total momentum is the sum of the momentums of both pieces.

Total Momentum after explosion = (m1 * v1_x + m2 * v2_x) ** i + (m1 * v1_y + m2 * v2_y) ** j + (m1 * v1_z + m2 * v2_z) ** k

Therefore, we can equate the total momentum before and after the explosion to find the values of v2_x, v2_y, and v2_z.

(a) The velocity of the other piece, in unit-vector notation, is v2 = (v2_x) ** i + (v2_y) ** j + (v2_z) ** k. We can determine these values by solving the equations we derived above.

(b) The kinetic energy of the other piece can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Substitute the values of mass and velocity into the formula, and you'll get the answer in joules (J).

(c) To find the kinetic energy produced by the explosion, we need to calculate the change in kinetic energy. So, subtract the total initial kinetic energy (which is the sum of the kinetic energies of both pieces before the explosion) from the total final kinetic energy (which is the sum of the kinetic energies of both pieces after the explosion).