A futuristic magnetic levitation train weighing 4.5 × 10 ⁴ kg is moving at 0.81c (c is the speed of light). The rate of change of energy with respect to speed (dE/dv) represents the energy needed for each 1.0 m/s increase in speed. Determine the extra energy required to raise the train's speed by 1.0 m/s.

In terms of c (the speed of light), at what speed does a nano-probe used in medical treatment have kinetic energy that is twice greater than what would be predicted by classical mechanics?

Consider a hypothetical particle physics scenario where a newly discovered particle puyon moves to the right at 0.85c, and its antiparticle (anti-puyon) moves to the left at the same speed. Upon collision, they annihilate each other and produce four gamma-ray photons (equal energies). Determine the wavelength of these photons. The rest mass of a puyon (or anti-puyon) is approximately 1.53 × 10 ^-27 kg.

A person stands on the rear end of a boat, moving away from the shore. A person can throw a frisbee at 25 m/s. They throw the frisbee towards the shore, and it approaches at a speed of 15 m/s. What is the boat's speed?