In a science fiction novel two enemies, Bonzo and Ender, are fighting in outer spce. From stationary positions, they push against each other. Bonzo flies off with a velocity of +1.7 m/s, while Ender recoils with a velocity of -3.3 m/s. Determine the ratio mBonzo/mEnder of the masses of these two enemies.
To determine the ratio mBonzo/mEnder of the masses of Bonzo and Ender, we can use the principle of conservation of momentum. The principle states that the total momentum before the interaction is equal to the total momentum after the interaction.
The momentum of an object is defined as the product of its mass and velocity. Therefore, the momentum before the interaction can be expressed as:
Initial momentum = mBonzo * 0 (since Bonzo is stationary) + mEnder * 0 (since Ender is also stationary)
After the interaction, Bonzo flies off with a velocity of +1.7 m/s, while Ender recoils with a velocity of -3.3 m/s. Thus, the final momentum can be expressed as:
Final momentum = mBonzo * 1.7 + mEnder * (-3.3)
Since the principle of conservation of momentum states that the initial momentum is equal to the final momentum, we can set up the following equation:
0 = mBonzo * 1.7 + mEnder * (-3.3)
Simplifying the equation, we get:
1.7mBonzo = 3.3mEnder
Now, we can solve for the ratio mBonzo/mEnder:
mBonzo/mEnder = 3.3/1.7
Evaluating this expression, we find:
mBonzo/mEnder ≈ 1.94
Therefore, the ratio of the masses of Bonzo to Ender is approximately 1.94.