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Yang (60 kg), traveling at 3 m/s and not watching where she is going, bumps into Alka (75 kg) who is traveling in the opposite direction at 2 m/s. They travel together after the collision. They hit a bush and take 0.75 seconds to stop.

- What is their velocity immediately after they bump into each other?

Use the equation for conservation of momentum:

\[ M_1V_1 + M_2V_2 = (M_1 + M_2)V \]

Substitute the given values:

\[ (60 \, \text{kg} \times 3 \, \text{m/s}) + (75 \, \text{kg} \times -2 \, \text{m/s}) = (60 \, \text{kg} + 75 \, \text{kg})V \]

This simplifies to:

\[ 180 \, \text{kg m/s} - 150 \, \text{kg m/s} = 135 \, \text{kg} \times V \]

\[ 30 \, \text{kg m/s} = 135 \, \text{kg} \times V \]

Solving for \( V \), we get:

\[ V = \frac{30}{135} \, \text{m/s} \approx 0.22 \, \text{m/s} \]

- Can you please explain more in-depth how the instructor got 135 and then 0.22 m/s as a result?

The value 135 kg is the combined mass of Yang and Alka after they collide (60 kg + 75 kg = 135 kg). The velocity 0.22 m/s is calculated by dividing the net momentum (30 kg m/s) by the total mass (135 kg), resulting in approximately 0.22 m/s.

Answer :

The instructor's calculation of 135 kg represents the combined mass of Yang and Alka after bumping into each other. The velocity immediately after collision, 0.22 m/s, was found using the conservation of momentum formula, and it indicates the pair's shared velocity immediately post-collision.

The instructor calculated the velocity immediately after two people bump into each other using the principle of conservation of momentum. The total mass after Yang and Alka collide is the sum of their masses, which is 60 kg + 75 kg = 135 kg. To find the velocity (V(1,2)) after the collision, the total momentum before the collision must equal the total momentum after the collision. The calculation for the total momentum before the collision uses the velocities and masses of Yang and Alka moving in opposite directions, where Alka's velocity is negative because it's in the opposite direction. The equation is: (60 kg imes 3 m/s) + (75 kg imes -2 m/s) = 135 kg imes V(1,2), which simplifies to 180 kg ext{m/s} - 150 kg ext{m/s} = 135 kg imes V(1,2). This results in 30 kg ext{m/s} = 135 kg imes V(1,2), and thus V(1,2) = 30 kg ext{m/s} / 135 kg = 0.22 m/s.

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