When ignoring the antineutrino, the simplified equation for the decay of Cobalt-60, which is initially at rest, into Nickel-60 can be written as:

⁶⁰Co → ⁶⁰Ni + e⁻

Formulate an equation that represents the conservation of relativistic momentum for this decay equation. Your equation should be written in the units of speed (v).

A source of coherent and directional light emits a beam of photons (event A) from Earth toward a detector fixed on the surface of Mars. Event B occurs when the beam hits the detector. Calculate the spacetime interval between events A and B. Consider that the distance between Earth and Mars is 2.26 × 10 ⁸ km.

An aircraft warning light on the top of a tower blinks once every 2.0 s. A child in a bus, moving at a constant speed in the horizontal direction, first sees the light at a distance of -15 m from their seat and then sees it again 2.0 s later at a distance of +15 m from their seat. Determine the speed of the bus relative to the tower.

Specialized nano-probes developed for specific therapeutic applications have a rest half-life of 3.0 μs, but when accelerated to near-light speeds, their half-life extends to 6.0 μs. These nano-probes are 300 times as massive as a proton. What's the total energy of a fast-moving nano-probe?

A man is on a train moving at 4.0 m/s. He can throw a ball at a speed of 7.0 m/s. What is the ball's speed relative to the ground if he throws the ball (i) in the direction the train is moving, (ii) in the opposite direction of the train's movement, and (iii) When the ball is thrown perpendicular to the direction of the train's movement.

An aircraft flies 5900 km per day around Earth at 210 m/s. The aircraft returns to its starting point 4 days later at the same speed. How much has the pilot aged compared to their airbase colleagues? Hint: Use the binomial approximation.

In order to coordinate clocks in a reference frame, a light beam is activated at the origin when t = 0 s. What initial time value should be assigned to the timepiece positioned at the spatial coordinates (x, y, z) = (0 m, 35 m, 15 m)?

In a controlled experiment, a particle is launched to the left at a velocity of 0.70c. At the same time, a different particle moves to the right at a speed of 0.50c. What is the speed of the first particle, as a fraction of the speed of light (c), relative to the second particle?

A race of spaceships is conducted by scientists on earth. Spaceship A takes off first at 0.400c relative to the earth. Spaceship B takes off a while later at 0.720c, measured relative to the earth and in the same direction as spaceship A. i) If spaceship B should catch up with spaceship A, what is the direction (toward or away from) of spaceship A velocity relative to spaceship B. ii) Determine the velocity magnitude of spaceship A measured by a pilot in spaceship B. 

In an inertial reference frame S, a spacecraft X of mass 10M is stationary. Without any external influence, the spacecraft undergoes a spontaneous fission event, splitting into two fragments: spacecraft Y, with mass 2M, is propelled to the right with a velocity of 0.6c relative to S, while Spacecraft Z, with mass 8M, is driven to the left with a velocity of 0.15c relative to S to ensure the conservation of momentum. An observer is situated in another inertial frame S', which is moving rightward with a speed of 0.3c relative to the original reference frame S. Using the Lorentz velocity transformation, determine the velocities and the Newtonian momenta of Y and Z in reference frame S'.