A projectile flies out of the gun at an angle of 30 degrees to the horizon. One hundredth of the total work of the powder

A projectile flies out of the gun at an angle of 30 degrees to the horizon. One hundredth of the total work of the powder gases is spent on recoil. How many times is the weapon heavier than the projectile?

Impulse conservation law:
m1 * v1 = m2 * v2 * cos alpha
Propellant gases work:
A2 = m2 * v2 ^ 2/2
Recoil work:
A1 = m1 * v1 ^ 2/2
A1 / A2 = m1 * v1 ^ 2 / m2 * v2 ^ 2 = 1/100
Total:
m1 / m2 = v2 * cos alpha / v1
(system)
v2 / v1 = 10 √ (m1 / m2)
m1 / m2 = 10 √ (m1 / m2) * cos alpha = 100 cos ^ 2 alpha = 100 cos ^ 2 30 = 75
Answer: 75