Velocity and Momentum in Action

What happens when a boy pushes a girl on a skating rink?

What is the final velocity of the girl and how does it affect the boy?

Answer:

The final velocity of the girl is 6.5 m/s, while the boy will have a velocity of 6.5 m/s in the opposite direction.

When a 65.0-kg boy pushes a 40.0-kg girl on a skating rink, the girl is sent eastward with a speed of 4.00 m/s. According to the law of conservation of momentum, the total momentum before and after the interaction should be the same.

Using the equation [m_bv_ib + m_gv_ig = m_bv_fb + m_gv_fg], where m represents mass and v represents velocity, we can calculate the final velocity of the girl. Substituting the known values of masses and initial velocity of the girl, we find that the final velocity of the girl is 6.5 m/s.

Since momentum is conserved, the boy will also have a velocity of 6.5 m/s in the opposite direction. This demonstrates how actions and reactions are equal and opposite in nature, as described by Newton's third law of motion.

Velocity is defined as the rate of change of displacement with respect to time, and it is a vector quantity that includes both magnitude and direction. Understanding the concepts of momentum and velocity is crucial in analyzing the dynamics of interactions between objects in motion.