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.

a. How fast was the rocket climbing when the engine stopped?

rock1

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 censor stop. The graph shows the velocity of the water rocket during its flight. How fast was the rocket moving when the water finished propelling it upwards? Awesome. So it appears our final answer that we're ultimately trying to solve for is we're trying to determine how fast was this particular rocket moving when the water finished propelling it upwards. So that's our final answer we're ultimately trying to solve for how fast was this rocket moving when the water finished pushing it up into the air. So with that said, Our first order of business in order to understand how to properly solve this problem, we need to investigate our graph that is provided to us. And as you can see, our Y axis denotes the velocity in feet per second. And our X-axis denotes the time in seconds. And we have our curve represented in red, which shows the velocity of the water rocket during its flight. And as you can see, it starts from rest at 0.0, so our curve starts at the origin point. It starts from rest. And then it slowly starts to ascend up into the air, so it starts to increase, increase, increase until it reaches a point where it doesn't increase or go upwards anymore because it reaches its maximum height, and that's when the water expulsion ends, and then we have a straight diagonal line pointing downwards, indicating that's when our water rocket. Is losing its upward momentum and it's falling back down to the ground. So with that said, with that in mind, let us first denote time as T, so we're gonna call time T, and let us denote the velocity as V. And from our graph, as we should note and recall, 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 upward motion. And let us also note that at 0. 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 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, with that in mind, let us note, I'll use a plus sign for positive and I'll use a negative sign to represent decreasing. Awesome. So with that said, therefore, as a result, as we should note and recall, the water was expelled and was accelerating at 0 is less than T and T is less than 3. And as it continues its upward movement, so this means that it continued at its upward movement. However, we need to note that it was slowing down at 3 is less than T and T is less than 7. So we need to therefore, as a result, note and recall that as the water finishes propelling the rocket upward, At T equals 3, and we need to note that at T equals 3, the corresponding velocity will be equal to 120 ft per second. And we can see this as the we can see this as the parentheses 3120 on our graph, which this point I'll circle it in blue. is when we go to T equals 3, and then we go up to 120, and that is the peak of our curve. So that will mean our final answer, without a doubt has to be our velocity is equal to 120 ft per second. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in our next video. Bye.

Key Concepts

Velocity

Acceleration

Graph Interpretation

Watch next