I want to solve the problem shown in the following figure 51

I want to solve the problem shown in the following figure 5-1

explain in detail

Shock speed S = (gamma+1)*V/4 + sqrt (gamma+1)^2*V^2 / 16 + a1 ^2)

a1 = sqrt (gamma*R*T) = sqrt (1.4*287*298) = 346.0295 m/s

S = (1.4+1)*500/4 + sqrt ((1.4+1)^2 * 500^2 / 16 + 346.0295^2)

S = 757.9699 m/s

Here, S = 2V

V = 2*(2V)*(1 – (a1 / (2V))^2) / (gamma+1)

Simplifying it we get, V = a1 / sqrt( 3- gamma)

V = 346.0295 / sqrt(3 – 1.4) = 273.5603 m/s