Final answer:
An object with a relativistic momentum 8.50 times greater than its classical momentum is moving at approximately 0.992 times the speed of light (c).
Step-by-step explanation:
The question involves the concept of relativistic momentum in physics, where an object's momentum at high velocities near the speed of light can differ significantly from its classical (Newtonian) momentum. According to the information provided, an object has a relativistic momentum that is 8.50 times greater than its classical momentum. To find its speed, we use the relativistic momentum formula which incorporates the Lorentz factor, γ (gamma).
In relativistic mechanics, the momentum p is given by p = γmv, where m is the rest mass of the object, v is the velocity, and γ is the Lorentz factor given by γ = 1 / √(1 - (v^2/c^2)). The classical momentum, on the other hand, is simply p = mv. Since we know that the relativistic momentum is 8.50 times the classical momentum, we can create a ratio of γ = 8.50. By solving for v in the Lorentz factor formula with γ set to 8.50, we can determine the object's velocity.
After solving the equation for γ, we find that the speed of the object is approximately 0.992c, where c is the speed of light (approx 3 x 108 m/s). This means the object is traveling at approximately 99.2% of the speed of light.