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.

d. When did the parachute pop out? How fast was the rocket falling then?

rock4

Accepted Answer

Below there. Today we're gonna 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. When did the rocket hit the tree? What was its velocity at this point? Awesome. So it appears for this particular problem, we're ultimately trying to figure out at what exact time did the rocket strike or hit the tree. And our second answer is we're also asked to figure out what was its velocity when the rocket hit the tree. So with that said, now that we know that we're trying to solve for two separate answers, at what time the rocket hit the tree and what was the velocity when the rocket hit the tree. Let us quickly look at our graph to help us better visualize what is occurring for this particular problem to help us solve for our final two answers. As you can see, we have our curve represented by a bold black line, and as you can see, 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, so it starts at the origin point, which is at 0.0, and as it starts to ascend, it slowly starts to curve upwards till it reaches its peak, where it reaches the highest point that it descends. Which it means as high up as it can go, once the water expulsion ends, so the water expels it upwards into the air till the water runs out, and then it briefly goes up just a little bit more, and then it falls back to earth. And as it's falling back to earth, we have a very steady solid decline. Awesome. So with that said, now that we have a visualization of what's happening in this particular prompt, let us first denote time as T, and let us also denote velocity as V, respectfully, and we need to note and recall that it is stated that a sensor was used to track the velocity of this particular water rocket. So with that in mind, when the rocket hits the tree, the sensor stops. So since the graph only extends from T equals 0 to T equals 9, that will mean that the rocket hits the tree at T equals 9 seconds. Fantastic, logically speaking. So to say that again, so we need to note that when the rocket hits the tree, the sensor will stop working. So we can see from our graph that it extends from T equals 0 seconds to T equals 9 seconds. So that means logically speaking, since the sensor stops working when it hits the tree, that means that the time it stops working is at T equals 9 seconds. And the corresponding velocity, when we follow T equals 9 seconds and we go down, that will mean that the corresponding velocity is -60 ft per second, and I'll circle that point in green on our graph. So that will mean that our corresponding velocity will be equal to -60 ft per second. And that's it. Those are our final two answers. Hooray, we did it. So to quickly recap, the corresponding velocity at T equals 9 seconds will be -60 ft per second, and we can see this at the parentheses 9.60 on our provided graph. And that's it. We've officially solved for this problem. 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

Acceleration

Graph Interpretation

Watch next