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.

c. When did the rocket reach its highest point? What was its velocity then?

rock3

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. At what time did the rocket arrive at its maximum height value? What was its velocity value at this specific point? Awesome. So it appears for this particular problem we're asked to solve for two separate answers. Our first answer is we're trying to figure out at what specific time did the rocket arrive at its maximum height value. That's our first answer. And then we're also asked to solve for the velocity value at the specific point when our rocket reaches its maximum height value. So with that said, now that we know we're trying to solve for two separate answers, let's investigate our graph that is provided to us because it will help us solve for this particular problem. As you can see, our Y axis denotes our velocity in units of feet per second. And our x-axis denotes the time in units of seconds. And then we have our curve, which denotes the flight path of our rocket, which once again this is denoting our velocity of the water rocket during its flight to be precise. And as you can see, our rocket starts from rest, so that means our curve starts at 0.0 at the origin point, and as it starts to ascend, it curves upwards and until it reaches its peak value. And then it will start to descend once it expels all the water, that's propelling it upwards, and then it will go up just a little bit more, and then it'll just start to fall back to the earth, means it doesn't have the water pushing it upwards anymore. So now, as we now that we have a good visualization of what's happening for this particular problem, let us quickly denote time as T and let us denote V as velocity, and let us note, as we should recall a note from our graph, that the velocity will be positive at 0 is less than T and T is less than 7. And as we should recall, a positive velocity will indicate an upwards motion, and we need to note that at 0 is less than T and T is less than 3. We need to note that the velocity will increase, and we also need to note that at 3, is less than T and T is less than 7, we need to note that the velocity will decrease. So I'm using a plus sign to denote increase and a negative sign to denote decreasing. So therefore, as a result, we should note that the water was expelled and was accelerating at 0 is less than T and T is less than 3, and as it continued its upward movement but was slowing down at 3. is less than T and T is less than 7. So therefore, without a doubt, we can go ahead and state that the velocity will be negative at 7 is less than T and T is less than or equal to 9. And once again we need to recall a note that a negative velocity will indicate a downwards motion. So therefore, without a doubt, the rocket was continuously ascending from T equals 0 seconds. 2, T equals 7 seconds. Where it reaches its maximum height. So therefore, the velocity at T equals 7 seconds. So at T equals 7 seconds, the velocity will be V is equal to 0 ft per second, and those are final two answers. Hooray, we did it. So once again, to quickly recap, As the velocity, so we need to note that our velocity at T equals 7 seconds is going to be 0 ft per second, and we can see this point at, and let's write this in blue, it'll be at the point 7.0 on our graph. So once again, as the rocket is continuously ascending from T equals 0 seconds to T equals 7 seconds, where it reaches its maximum height value, that will mean as a result, the velocity will be 0 ft per second. So once again, the velocity is 0 ft per second when T equals 7 seconds. And that's it. 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

Critical Points

Graph Interpretation

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