Final answer:
The problem is a Physics problem about kinetic energy and the relationship between mass and velocity. The father's original speed can't be calculated without additional numerical values, although the relationships between his and the son's kinetic energies and masses provide the equations needed to find their speeds.
Step-by-step explanation:
You're dealing with a classic physics problem that involves understanding kinetic energy (KE) and mass-speed relationships. Kinetic energy is given by the formula KE = 1/2 mv², where m is mass and v is velocity. If the father has 1/2 the kinetic energy of the son and the son has 1/3 the mass of the father, with the father's mass being m and his speed being v, the son's mass is m/3 and his speed can be represented as u. The initial kinetic energies can be written as:
- Father's KE = 1/2 m*v²
- Son's KE = 1/2 (m/3)*u²
We know Father's KE is 1/2 of Son's KE, which means:
1/2 m*v² = 1/4 (m/3)*u² -> 3v² = u²
After the father speeds up by 1.7 m/s, their kinetic energies are equal, thus:
1/2 m*(v + 1.7)² = 1/2 (m/3)*u²
By solving these equations, you can find the original speeds of the father and son. However, without additional information or numerical values, we can't solve for the exact speeds.