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When a body explodes, it breaks into several parts. This phenomenon is an interesting scenario of an energy transformation, particularly from the point of view of physics. During an explosion, a single object disintegrates into multiple fragments with significant force. This transformation involves changes in physical properties such as velocity, direction, and distribution of mass.
In the context of our exercise, a 1 kg body undergoes an explosion, breaking into three different pieces. The fragmentation process leads to an entirely new system where conservation laws play a critical role in understanding the resultant motion of each piece. While energy is not necessarily conserved due to the explosive forces, momentum is always conserved in such processes, a fact we can rely on to calculate unknown quantities.
The explosion is characterized by the release of potential energy, which gets converted into the kinetic energy of the fragments, propelling them in different directions. This results in various velocities and sometimes considerably complex dynamics, which can be unravelled using physics principles.

The Pythagorean Theorem is a fundamental concept in mathematics. It plays a crucial role in relating the sides of a right-angled triangle. For a triangle with sides of length a, b, and hypotenuse c, the theorem states: \[ a^2 + b^2 = c^2 \]In the exploding body scenario, the pieces of equal mass fly perpendicular to each other. Hence, they form a right-angled triangle with their velocities as the two legs. Using the Pythagorean Theorem, we determine the resultant momentum direction and magnitude.
This application is essential because both fragments shoot out at right angles with the same speed, creating a 90-degree junction. By calculating the square of each momentum component and summing them, the theorem allows us to find the resultant momentum, which dictates the motion necessary to maintain overall momentum balance for the system.

Vectors are quantities that have both magnitude and direction, crucial in understanding motion, especially in multiple dimensions. In our problem, velocity is a vector quantity, making its analysis essential in determining the outcome.
Each of the smaller fragments travels with a velocity of 15 m/s in perpendicular directions. We must decompose these into vector components to analyze their motion. The first component is along the x-axis, while the second is along the y-axis. The third, unknown velocity of the heavier fragment acts to balance these components. Through vector analysis, summing these components helps maintain the law of conservation of momentum.

• Using vector components ensures we consider both direction and magnitude for all motion-related problems.
• This concept also acts as a foundation for utilizing the Pythagorean Theorem effectively, as vectors form the sides of the involved triangle.

Mass ratio is a crucial element in understanding how different parts of a system interact during separation events, like explosions. In this problem, a mass ratio of 1:1:3 involves understanding how this proportion affects the momentum distribution.
First, it helps determine the individual masses of the fragmented pieces. Given that the total mass is 1 kg, their masses can be calculated in terms of this ratio, leading to masses of \(\frac{1}{5}\) kg, \(\frac{1}{5}\) kg, and \(\frac{3}{5}\) kg. This calculation allows us to apply the conservation of momentum accurately, as each fragment's mass determines the extent of influence each has on the system's total momentum.
Such ratios are prominent in a variety of physics problems. They are often used to simplify complex interactions by focusing on proportional relationships rather than absolute values, making calculations more straightforward and comprehensible.