calculate the force exerted on a rocket given that the propelling gases are expelled at a rate of 1500 kg/s with a speed of 4.0x10^4 (at the moment of take off)

we know that momentum is given as

P = mv

where P = momentum, m = mass, v = velocity

taking derivative both side relative to "t"

dP/dt = v (dm/dt)

we know that : dP/dt = F = force

hence

F = v (dm/dt)

given that:

dm/dt = rate of mass expelled = 1500 kg/s

v = velocity = 4 x 10⁴ m/s

hence, inserting the values in the above formula

F = (4 x 10⁴) (1500)

F = 6 x 10⁷ N