## Emily778 one year ago when serving in tennis a player tosses the tennis ball vertically in the . The height h of the ball after t seconds is given by the quadratic function h(t)=-5t^2+7t (the height is measured in meters from the point of the toss.) a. How high in the air does the ball go? b. Assume that the player hits the ball on its way down when it's 0.6m above the point of the toss. For how many seconds is the ball in the air between the toss and the serve? I've already got -7/2x(-5)=7/10-.7

1. Emily778

@Nurali

2. Emily778

@Hero

3. ranga

For part a) h(t)=-5t^2+7t =-5(t^2 - 7/5t) complete the square of the expression in parenthesis to put the function in the vertex form. Then comparing it to standard vertex form: h = a(t-h)^2 + k where (h,k) is the vertex. Identify k and that will be how high the ball goes.

4. Emily778

I already told you I have .7

5. ranga

First you put that under b. Secondly, that is not k. You have h.

6. Emily778

What do I do next?

7. ranga

plug in t = .7 in h(t)=-5t^2+7t and calculate h

8. dan815

lol

9. dan815

there used to be constantly questions about slopes and lines now i see these questions a lot

10. dan815

when you throw a ball up in the air at the highest point its velocity = 0 as it is goes up going up to down, so somwhere in there it has 0 speed and velocity

11. dan815

so h'(t) = velocity set h'(t) = 0 and solve

12. dan815

that tells you the time it takes to get to highest veloicty then see what distance you travel given that time substituting that time into h(t)

13. dan815

that highest point*, with 0 velocity

14. Emily778

@ranga I got 5.145 for h. Is that right?

15. dan815

oh is this precalc?

16. ranga

Try again. Don't forget there is a negative sign in front of t^2.

17. ranga

-5t^2+7t -5(0.7)^2 + 7(.7) = ?

18. Emily778

Now you tell me...

19. ranga

You can evaluate that using your calculator.

20. Emily778

okay, I got 2.45?

21. Emily778

@ranga

22. Emily778

hello?????????

23. ranga

BTW, the notifications are not working for a couple of days and so people may not be notified when tagged or a reply is posted. Yes 2.45 meters is correct for a) For b) substitute h = 0.6 in h(t) = -5t^2+7t and solve for t. You will get two values for t -- the ball reaches 0.65 meters once while going up and once while coming down. Choose the higher t because they want the value when the ball is coming down.