Understanding the Physics

* Conservation of Energy: The total mechanical energy of the arrow remains constant throughout its flight (ignoring air resistance). This energy is the sum of its kinetic energy (energy of motion) and potential energy (energy due to its height).

* Kinetic Energy: KE = (1/2) * mv² (where m is mass and v is velocity)

* Potential Energy: PE = mgh (where g is the acceleration due to gravity, approximately 9.8 m/s², and h is height)

Calculations

1. Final Energy: At its highest point (130 m), the arrow momentarily stops, so its kinetic energy is zero. Its total energy is purely potential energy:

PE_final = mgh = (0.03 kg) * (9.8 m/s²) * (130 m) = 38.22 J

2. Initial Energy: The initial energy is the sum of its kinetic energy (what we want to find) and its potential energy (which is zero at the ground):

E_initial = KE_initial + PE_initial = (1/2) * mv² + 0

3. Equating Energies: Since energy is conserved, the initial energy equals the final energy:

E_initial = E_final

(1/2) * mv² = 38.22 J

4. Solving for Initial Velocity:

v² = (2 * 38.22 J) / (0.03 kg) = 2548

v = √2548 ≈ 50.48 m/s

Therefore, the initial velocity of the arrow is approximately 50.48 m/s.