What is the Final Velocity of the 18 kg Rock After Collision in Space?

[syjxpatty]

Homework Statement

In outer space a rock with mass 4 kg, and velocity < 4000, -2800, 3400 > m/s, struck a rock with mass 18 kg and velocity < 250, -290, 260 > m/s. After the collision, the 4 kg rock's velocity is < 3600, -2300, 3900 > m/s.
What is the final velocity of the 18 kg rock?

Homework Equations

Momentum Principle

pf = pi + Fnetdeltat

The Attempt at a Solution

Please help me if you can! I am pretty frustrated with this problem and I don't know why I am getting it wrong! I used the momentum principle, but it hasnt worked since this is a collision problem. Should I use that the final speed for the 18kg rock is v2f = 2(m/M)v1i

v2 being the final velocity of 18kg
v1 being the initial velocity of 4kg

 

[Google_Spider]

Hi, Write the velocities in vector form. Like for 4 Kg rock, initial velocity will be

$$V_4=4000i-2800j+3400k$$

Then apply

$$P_i=P_f$$

 

[Moetasim]

I can provide a response to this problem by using the principles of momentum and conservation of energy. In this scenario, we have two rocks colliding with each other in outer space. The initial velocities and masses of both rocks are given, and we are asked to find the final velocity of the 18 kg rock after the collision.

To solve this problem, we can use the momentum principle, which states that the total momentum of a system remains constant unless acted upon by an external force. In this case, we can consider the two rocks as a closed system, where the total momentum before the collision is equal to the total momentum after the collision.

Using the equation for momentum, we can write:

pf = pi

Where pf is the final momentum of the system and pi is the initial momentum of the system. We can also express momentum as the product of mass and velocity:

pf = m1v1f + m2v2f

pi = m1v1i + m2v2i

Where m1 and m2 are the masses of the two rocks, and v1i, v1f, v2i, and v2f are the initial and final velocities of the two rocks, respectively.

Substituting the given values in the equations, we get:

(18 kg)(v2f) = (4 kg)(3600 m/s) + (18 kg)(250 m/s)

Solving for v2f, we get:

v2f = 400 m/s

Therefore, the final velocity of the 18 kg rock after the collision is < 400, -280, 260 > m/s.

We can also use the conservation of energy principle to solve this problem. In a closed system, the total energy remains constant. Therefore, we can equate the initial kinetic energy of the system to the final kinetic energy of the system.

Using the equation for kinetic energy, we can write:

KEi = KEf

Where KEi is the initial kinetic energy of the system and KEf is the final kinetic energy of the system. We can express kinetic energy as 1/2mv^2:

1/2m1v1i^2 + 1/2m2v2i^2 = 1/2m1v1f^2 + 1/2m2v2f^2

Substituting the given values, we get:

1/2