Sketching a graph from a function

[Specter]

Homework Statement

The path of a baseball relative to the ground can be modeled by the function d(t)=-t²+8t+1 where d(t) represents the height of the ball in meters, and t represents time in seconds.

a. Sketch a grpah of the function between 0 and 9 seconds.
b. What is the speed of the ball when it hits the ground?

Homework Equations

The Attempt at a Solution

I have no idea how to do this. It's in the first unit of my calculus class. I tried creating a table of values and then plotting the points but that didn't work. I also tried solving for d(0) through d(9) and then plotting the points but that gave me different answers then what others were getting. Any help on where I should start would be great, thanks.

 

[scottdave]

Plugging in points and connecting the dots is one way to get an idea of what the graph is doing.
Let's start with this. Do you know what type of function it is? If it were something like y= -x²+8x+1 would that be easier to sketch (rather than picking a bunch of points)?

As far as the speed of the ball, are they looking for just the vertical speed?

Oh yes, can you post a picture of your attempt?

 

[Mark44]

Homework Statement

The path of a baseball relative to the ground can be modeled by the function d(t)=-t²+8t+1 where d(t) represents the height of the ball in meters, and t represents time in seconds.

a. Sketch a grpah of the function between 0 and 9 seconds.
b. What is the speed of the ball when it hits the ground?

Homework Equations

The Attempt at a Solution

I have no idea how to do this. It's in the first unit of my calculus class. I tried creating a table of values and then plotting the points but that didn't work.

Why didn't it work? There's nothing wrong with this approach. The table should have pairs of values (t, d(t)). To plot a point, the t value is along the horizontal axis, that the d(t) value is along the vertical axis.

I also tried solving for d(0) through d(9)

You're not "solving" for d(0) etc. -- you're evaluating the distance function at 0, 1, and so on.

and then plotting the points but that gave me different answers then what others were getting. Any help on where I should start would be great, thanks.

Please show us what you got. One of the rules here is that you have to show us what you've tried, not just describe what you're done in general terms.

 

[Specter]

Plugging in points and connecting the dots is one way to get an idea of what the graph is doing.
Let's start with this. Do you know what type of function it is? If it were something like y= -x²+8x+1 would that be easier to sketch (rather than picking a bunch of points)?

As far as the speed of the ball, are they looking for just the vertical speed?

Oh yes, can you post a picture of your attempt?

Why didn't it work? There's nothing wrong with this approach. The table should have pairs of values (t, d(t)). To plot a point, the t value is along the horizontal axis, that the d(t) value is along the vertical axis.
You're not "solving" for d(0) etc. -- you're evaluating the distance function at 0, 1, and so on.

Please show us what you got. One of the rules here is that you have to show us what you've tried, not just describe what you're done in general terms.

I figured out the graphing part. I forgot to add the square on a few of them so it messed everything up. For part b, I don't know what speed they are asking for. All the question asked for was the speed of the ball when it hits the ground. Can I use v=d/t to solve that? I don't know the horizontal distance so I don't think that I can use v=d/t.

If a picture of my graph is still needed, I can upload it here.

 

[Mark44]

For part b, I don't know what speed they are asking for. All the question asked for was the speed of the ball when it hits the ground. Can I use v=d/t to solve that?

No, they're looking for the instantaneous speed. You said you're in a calculus class. Possibly they have talked about velocity at this point, which would be d'(t), the derivative of the distance/displacement function.

 

[Specter]

No, they're looking for the instantaneous speed. You said you're in a calculus class. Possibly they have talked about velocity at this point, which would be d'(t), the derivative of the distance/displacement function.

Would I be able to use the limit formula to solve this question? I guess I would first need to determine when exactly the ball hits the ground because I need d(a) and d(a+h).

 

[Mark44]

Would I be able to use the limit formula to solve this question?

Yes. That might be the only formula you have, as this is the first unit.

I guess I would first need to determine when exactly the ball hits the ground because I need d(a) and d(a+h).

I'm not sure what you mean here. The ball hits the ground when d(t) = 0. Solve that equation for the value of t that gives a distance of 0.