Aproton moves along the x-axis in the laboratory with velocity uy = 0.6c. an observer moves with a velocity of v=0.8c along the direction of motion of the proton. a. what is the total energy of the proton in the lab frame? b. what kinetic energy does the observer measure for the proton? c. what momentum (in units of mev/c) does the observer measure for the protons?

Explanation:

Given that,

Velocity of the proton in lab frame

Velocity of the observer v= 0.8c

We need to calculate the velocity of the proton with respect to the observer

Using formula of velocity

(a). We need to calculate the total energy of the proton in the lab frame

Using formula of kinetic energy

Where, Proton mass energy = m₀c²

Put the value into the formula

(b). We need to calculate the kinetic energy of the proton in the observer

Using formula of kinetic energy

(c). We need to calculate the momentum of the proton with respect to observer

Using formula of momentum

We know that,

Proton mass energy = m₀c²

Hence, This is required solution.

the only real purpose of sputnik 1 was to beat the us into space. we were getting close to launching a useful satellite, explorer 1 - which launched on january 31, 1958. the ussr had to beat that, so they launched sputnik 1 on october 4, 19

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .