Understanding Motion from Graphs

Launching a ...

Question

Understanding Motion from Graphs

Launching a Rocket When a model rocket is launched, the propellant burns for a few seconds, accelerating the rocket upward. After burnout, the rocket coasts upward for a while and then begins to fall. A small explosive charge pops out a parachute shortly after the rocket starts down. The parachute slows the rocket to keep it from breaking when it lands.

The figure here shows velocity data from the flight of the model rocket. Use the data to answer the following.

b. For how many seconds did the engine burn?

rock2

Accepted Answer

Hello there. Today we're going to solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A student is conducting an experiment with a water rocket. The rocket is launched vertically up and its velocity is tracked using a sensor. The expulsion of water accelerates it upward. When the water is fully expelled, the rocket briefly continues to ascend and then starts to fall. As the rocket descends, it accidentally hits a tree which makes the sensor stop. The graph shows the velocity of the water rocket during its flight. How long did the water expulsion last? Awesome. So it appears for this particular problem, we're ultimately trying to figure out how long this water expulsion part of this particular rocket experiment lasted timewise. So we're trying to figure out how long this water expulsion lasted. So now that we know what we're trying to solve for, let's take a moment here to investigate our graph that is provided to us. We have the flight path of our velocity of our water rocket represented by a red curve. And we should note that our Y axis denotes the velocity in units of feet per second, and our X-axis denotes the time in units of seconds. And as you can see, our rocket starts from rest since it's not moving, so it starts at the origin 0.00 or 0.0, and then it slowly starts to be propelled upwards into the air by the water expulsion, where it reaches its peak height, where it stops the ascension, it stops going up. And then as it starts to fall back to Earth, it's a diagonal, a straight decrease down until it stops moving completely, until the rocket stops falling completely. So, now that we have a nice visualization of what's happening in this particular problem, Our first step is let us denote time as T, and let us also denote V as velocity, respectfully, and let us also note that from our graph, the velocity will be positive at 0 is less than T and T is less than 7. And a positive velocity will indicate an upwards motion. So once again, a positive velocity indicates an upwards motion. And let us also note that at 0 is less than T and T is less than 3, the velocity will increase, and at 3 is less than T and T is less than 7, the velocity will decrease. So I'm using a positive symbol for increase and a negative symbol for decrease. So therefore, as a result, the water was expelled and was accelerating at 0 is less than T and T is less than 3 as it continues its upwards movement. However, it was slowing down at 3 is less than T and T is less than 7. So that will mean, without a doubt, that the water expulsion lasted for T equals 3 seconds, and that has to be our final answer. Hooray, we did it. So once again, without a doubt, the water expulsion lasted for a time frame of T equals 3 seconds, and that is our final answer. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Key Concepts

Velocity-Time Graphs

Acceleration

Area Under the Curve

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