In the first second of it's flight a rocket eject 1/60 of it's mass with a relative velocity of 2400 m/s (I) find acceleration (Ii)what final velocity if the ratio of initial to final mass 4 to 60s?

I. To find the acceleration, we can use the formula:

a = (change in velocity) / time

Given that the change in velocity is 2400 m/s and the time is 1 second, we can calculate the acceleration:

a = 2400 m/s / 1 s
a = 2400 m/s^2

Therefore, the acceleration of the rocket is 2400 m/s^2.

II. To find the final velocity, we can use the conservation of momentum principle. The initial momentum of the rocket is equal to the final momentum after the ejection of mass.

Initial momentum = Final momentum
(mass_initial * velocity_initial) = (mass_final * velocity_final)

Given that the ratio of initial to final mass is 4 to 60, we can write:

mass_initial = 4x
mass_final = 60x

Substitute these values into the momentum equation:

(4x * 0) = (60x * velocity_final)
0 = 60x * velocity_final
velocity_final = 0

Therefore, the final velocity of the rocket is 0 m/s.

(I) Acceleration:

Let the initial mass of the rocket be M.

Initial momentum = 0 (rocket is at rest)

After ejection of 1/60 of mass, the remaining mass is 59/60 M.

Ejected mass = M/60

Ejected mass velocity = -2400 m/s (negative sign indicates opposite direction)

Final momentum = (59/60 M) - v - (M/60) - 2400 m/s

By conservation of momentum,
0 = (59/60 M) - v - (M/60) - 2400 m/s
v = (M/59) - 2400 m/s
Acceleration (a) = v/t = 2400 m/s / 1 s = 2400 m/s²

(II) Final Velocity:

Ratio of initial to final mass = 4:60 = 1:15

Let the final mass be m.

Then, M = 15m

Using conservation of energy,
Initial kinetic energy = (1/2) - M - 0² = 0
Final kinetic energy = (1/2) - m - v^2

Since the total energy remains constant,
0 = (1/2) - m - v^2
v = 0

Therefore, the final velocity is 0 m/s.