# Find the initial velocity of a water rocket (mass changes)

## Homework Statement

Find the initial velocity of the boost phase (when water is coming out). Here is everything I know -
• Mass of rocket with no water is 0.13kg, mass of rocket with water is 1.1kg. The total length of the rocket is 0.48m.
• The time to the maximum point is 3.46 seconds, and total time of flight is 6.68 seconds. The duration of the boost phase is 0.4 seconds.
• The height reached at the end of the boost phase is 21.9m.

## Homework Equations

The kinematics equations.

## The Attempt at a Solution

I am aware that one of the kinematics equations must be used, however, at the end of the boost phase, final velocity is not zero, and I don't know the acceleration (I would say 9.8m/s^2, but doesn't that change?). With 2 variables missing, I don't see how I can solve for initial velocity. Knowing displacement and time, how can I figure this out? [/B]

Velocity of what? the rocket, the water? The initial velocity of the rocket must be zero unless you have an infinite acceleration.

Velocity of what? the rocket, the water? The initial velocity of the rocket must be zero unless you have an infinite acceleration.
The velocity of the rocket - the rocket has to have a velocity to take off, right?

I think that the water leaving the rocket will cause a reaction that will create a force that will accelerate the rocket from zero to some maximum value.

Think about this. If you are stationary in a car and then push on the accelerator the velocity of the car will be initially at zero and then accelerate to some value depending on the cars engine torque.

I suggest you Google "rocket equation" and see what you get.

haruspex
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Find the initial velocity of the boost phase
Are you sure this is the question asked? Please post the question word-for-word as given to you.

Are you sure this is the question asked? Please post the question word-for-word as given to you.
It was given as a table, and the words in the column said "initial velocity of rocket taking off".

haruspex
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2020 Award
It was given as a table, and the words in the column said "initial velocity of rocket taking off".
Then you have your answer in posts #2 and #3, but I would word it differently. Not that it has to have zero velocity to take, but that it will be zero in this context.

I would bet that what is wanted is the velocity of the rocket just after the boost phase. This can be determined by the time to reach the maximum height. After 0.4 seconds, the rocket is no longer accelerating. Now given the time to achieve maximum height you can determine the velocity just after the boost is over. This is what I think is wanted.

haruspex