Final answer:
To find the inverse f-1(10) for the relativistic mass function f(v), we solve for the speed v when the mass m is 10, resulting in v being slightly less than the speed of light.
The calculation involves setting m to 10, rearranging the equation, and solving for v, which yields the result as a fraction of the speed of light, will get f−1(10) = c √(99/100).
Step-by-step explanation:
The question is asking how to find the inverse of the function defining the relativistic mass of a particle in terms of its speed.
Given the function f(v) = m0 / √(1 - v2/c2), with m0 = 1 and f-1(10), we need to find the speed v when the mass m equals 10.
To find f-1(10), we set m equal to 10 and solve for v:
m = 10 = 1 / √(1 - v2/c2)
Squaring both sides, we get:
100 = 1 / (1 - v2/c2)
Therefore, 1 - v2/c2 = 1/100
v2/c2 = 1 - 1/100
= 99/100
v2 = (99/100)c2
v = c √(99/100)
Thus, f-1(10) = c √(99/100), which means the speed v is slightly less than the speed of light c.