Solving Speed of Objects Problem

[yankees26an]

Homework Statement

A bomb that is originally at rest blows apart into three pieces of equal mass. Two of the
pieces have velocities (12i + 24j) m/s and (30i - 24j) m/s. What is the speed of the third
piece?

Homework Equations

m1v1 + m2v2 + m3v3 = 3mv4 (assuming m is the same)

The Attempt at a Solution

Not really sure where to begin. I can find the speed of the 2 objects by finding the k direction, but that's it.

 

[Doc Al]

Hint: What's the total momentum of all three pieces?

 

[kerimek]

As a scientist, the first step in solving this problem would be to understand the concept of conservation of momentum. This principle states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the system consists of the three pieces of the bomb.

Next, we can use the given information to set up an equation using the conservation of momentum principle. This equation would be:

m1v1 + m2v2 + m3v3 = 3mv4

where m represents the mass of each piece and v represents the velocity of each piece.

Since we know that the mass of each piece is equal, we can simplify the equation to:

v1 + v2 + v3 = 3v4

Now, we can substitute the given velocities for v1 and v2, and solve for v3:

(12i + 24j) + (30i - 24j) + v3 = 3v4

42i = 2v3

v3 = 21i

Therefore, the speed of the third piece is 21 m/s in the i direction.

In conclusion, by understanding the concept of conservation of momentum and setting up the appropriate equation, we can solve for the speed of the third piece of the bomb. This solution not only helps us find the answer to the given problem, but it also showcases the importance of understanding fundamental principles in solving scientific problems.