[sim0nz12345]

Hi there, could you please help me with this confusing question:

After (t) seconds, a projectile is at height (h) metres where h(t)=300+24t-3t^(2). Find the rate of change of height at t=2,t=3 and t=4 seconds (use a time interval of 0.01) seconds. Then describe what is happening to the projectile. Sketch the path.

I wouldn't know find the rates of change using the time interval of 0.01 seconds and then I wouldn't know ow to sketch it.

Thanyou

[Capuchin]

I guess it wants you to, for t=2, find the height at t = 1.995 and at t = 2.005 and find the change in height, then you can divide this by 0.01 to find the change in height per second, which is th rate of change at t=2 in a time interval of 0.01.

Does that make sense?

[sim0nz12345]

No sorry it doesn't really make sense to me. -_-

[Capuchin]

That's okay, I hate the word "rate" because it can mean so many things in different contexts.

You must have example questions that you have worked through in class or something? What I wrote above is what I would do if I was given the question, but there are certainly something's your teacher might do differently.

[sim0nz12345]

Thanks anyway
Could you please do one for an example
That would be much appreciated

[Capuchin]

Okay let's see, we want the rate of change at t=2 in an interval of 0.01, so we need to take the height at t = 2-0.005 and t = 2+0.005

so this gives us h(1.995)=335.939925m and h(2.005)=336.059925m

so the change is 336.059925-335.939925 = 0.12m in 0.01 seconds.

so the rate of change is 0.12/0.01 = 12 meters per second

[sim0nz12345]

Oh cool
Thanyou so much for your help, much appreciated

[galactus]

We could also use the instantaneous rate of change of y w.r.t. x









Just a thought.