Final answer:
To find the original speeds of the father and son, we use the relationship between kinetic energy and speed. The original speed of the father was 2.5 m/s and the original speed of the son was 5.9 m/s, based on the given mass and kinetic energy relationships and the father's increase in speed.
Step-by-step explanation:
The student's question relates to calculating the original speed of two bodies (a father and son) based on their kinetic energy and mass relationship. The kinetic energy of a body is given by the equation KE = \(0.5\cdot m\cdot v^2\), where m is the mass and v is the speed.
Let's assume the father has a mass of m_f and an initial speed of v_f. The son has a mass of m_s = \((3/5)m_f\) and an initial speed of v_s. Initially, the father's kinetic energy (KE_f) is one-third the kinetic energy of the son (KE_s). After the father speeds up by 3.8 m/s, their kinetic energies become equal.
Given:
- KE_f = (1/3)KE_s
- KE_s = \(0.5 \cdot m_s \cdot v_s^2\)
- KE_f = \(0.5 \cdot m_f \cdot v_f^2\)
- m_s = \((3/5)m_f\)
We can set up the equations:
- KE_f = \(0.5 \cdot m_f \cdot v_f^2\) = (1/3) \left(0.5 \cdot \left(\frac{3}{5}m_f\right) \cdot v_s^2\right)
- \(0.5 \cdot m_f \cdot (v_f + 3.8)^2\) = \(0.5 \cdot m_f \cdot v_s^2\)After solving these equations, we find that:
- The initial speed of the father was 2.5 m/s.
- The initial speed of the son was 5.9 m/s.