Per forum rules, please post your attempt.JoeDGreat said:Homework Statement: A rocket is in outer space, far from any planet, when the rocket engine is turned on. In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s. What is the rocket's initial acceleration?
Relevant Equations: Vf-Vi = VeIn(Mi/Mf)
Help me solve... I'm getting errors here..
They are giving you the instantaneous rate of mass ejection at ##t=0##:JoeDGreat said:a = -Ve/Me × dM/dt
dM/dt = Mi/120 ÷ 1sec = -Mi/120sec
a =-2400/Mi ( -Mi/120) = 20m/s²
PS: This is the textbook solving but, I don't know how dM= Mi/120
Is it this statement that is giving you interpretive issues? They should have just said something to the effect of " at the instant of firing", or we are just to assume the mass flow rate as constant over the first second for the sake of simplicity (i.e. being able to find a solution).JoeDGreat said:In the first second of firing, the rocket ejects 1/120 of its mass with a relative speed of 2400m/s.
Initial acceleration refers to the rate at which a rocket's velocity changes when it first begins its ascent into space. It is typically measured in meters per second squared (m/s^2).
Initial acceleration can be calculated by dividing the change in velocity (measured in meters per second) by the change in time (measured in seconds). This can be represented by the formula a = Δv/Δt, where "a" represents initial acceleration, "Δv" represents change in velocity, and "Δt" represents change in time.
The initial acceleration of a rocket is affected by several factors, including the thrust of the rocket's engines, the mass of the rocket, and the force of gravity acting upon the rocket.
Initial acceleration is important in rocket launches because it determines how quickly the rocket can gain altitude and reach its desired destination. A higher initial acceleration allows the rocket to reach higher speeds and achieve escape velocity, which is necessary for leaving Earth's atmosphere and entering space.
Yes, initial acceleration can change during a rocket's flight. As the rocket expends fuel and becomes lighter, its initial acceleration may increase. Additionally, the force of gravity acting upon the rocket may also change as it travels further away from Earth's surface, affecting its initial acceleration.