Question

question 11 of 25
two water balloons of mass 0.75 kg collide and bounce off of each other without breaking. before the collision, one water balloon moved at a velocity of 3.5 m/s east, while the other moved at a velocity of 2.75 m/s west. after the collision, one balloon moves at a velocity of 1.5 m/s west. what is the velocity of the other water balloon?

a. 2.25 m/s east
b. 2.25 m/s west
c. 1.75 m/s east
d. 1.75 m/s west

Explanation:

Step1: Define Variables and Directions

Let east be positive and west be negative. Mass of each balloon \( m = 0.75 \, \text{kg} \). Initial velocities: \( v_{1i} = 3.5 \, \text{m/s} \) (east), \( v_{2i} = -2.75 \, \text{m/s} \) (west). Final velocity of one balloon: \( v_{2f} = -1.5 \, \text{m/s} \) (west). Let \( v_{1f} \) be the final velocity of the other balloon.

Step2: Apply Conservation of Momentum

Conservation of momentum: \( m v_{1i} + m v_{2i} = m v_{1f} + m v_{2f} \). Divide both sides by \( m \): \( v_{1i} + v_{2i} = v_{1f} + v_{2f} \).

Step3: Substitute Values and Solve

Substitute values: \( 3.5 + (-2.75) = v_{1f} + (-1.5) \). Calculate left side: \( 3.5 - 2.75 = 0.75 \). So, \( 0.75 = v_{1f} - 1.5 \). Add 1.5 to both sides: \( v_{1f} = 0.75 + 1.5 = 2.25 \, \text{m/s} \) (positive means east).

Answer:

A. 2.25 m/s east