Thread: rectilinear motion/arc length

I know the title is vague, but I'm not sure what this question is asking:

A toy rocket is launched from the top of the building, it's height above the ground after seconds is given by . Find the total distance traveled from launch to crash.

How would I go about finding that?

Look at this graph; it marks the path of the rocket.

http://www.wolframalpha.com/input/?i=Plot+-4.9x^2%2B19.6x%2B58.8

When will the crash occur? And how would you have proven this without using the graph? And can you find the distance?

Originally Posted by Quacky

Look at this graph; it marks the path of the rocket.

http://www.wolframalpha.com/input/?i=Plot+-4.9x^2%2B19.6x%2B58.8

When will the crash occur? And how would you have proven this without using the graph?

?

Edit: I'm not sure how I would find the distance.

That's right, but I realise that I'd misread your question.

If it's the distance that you're looking for, then you need to find how high up the rocket travelled (this can be read off of the graph, but it's obviously far better to use calculus to find the maximum of the graph, and then subtract the initial height), then you need to find the distance down it travelled (this is just the height of the maximum) and add those together.

Using the graph is inferior to calculus, but it does illustrate the problem. Have an attempt using calculus and see how you go.

Originally Posted by Quacky

That's right, but I realise that I'd misread your question.

If it's the distance that you're looking for, then you need to find how high up the rocket travelled (this can be read off of the graph, but it's obviously far better to use calculus to find the maximum of the graph, and then subtract the initial height), then you need to find the distance down it travelled (this is just the height of the maximum) and add those together.

Using the graph is inferior to calculus, but it does illustrate the problem. Have an attempt using calculus and see how you go.

The max height is 78.4m, so I'm assuming it's (78.4-58.8)+78.4? Hopefully I understood that correctly. Thanks a lot for your help!

Read here: Arc Length -- from Wolfram MathWorld

That's right, but I was assuming the question merely wanted the vertical distance travelled. Is this the case? If not, you'll have to use ASZ's method.