Word problem for maximum height

[vanillah]

1) In a baseball game,a batter pops a ball straight up in the air as given by the function: f(x)=-16t^2+160 where t is in seconds. A seagull is witnessed swooping down and swallowing the ball at an altitude of 300 feet. Find the time,t, when the seagull ate the ball.

2)The ball described in problem #1 will reach its maximum height before being eaten by the seagull. After how many seconds will the ball reach its maximum height and what will that height be?



Above are the two problems I need help with. Since they all involve the same formula I hope its okay to post them together.I have the answers for both problems since these are just from a practice workbook but it doesnt explain how to get to these answers. For the first problem
I tried 300=-16t+160t but the result was extremely off:t+10t=300
I also tried using the vertex of a parabola formula: -160/2(-16)=128

For the second problem I had no idea where to start.
Thanks for reading/helping in advance. I am so terrible at math x.x

 

[JeffM]

1) In a baseball game,a batter pops a ball straight up in the air as given by the function: f(x)=-16t^2+160 where t is in seconds. A seagull is witnessed swooping down and swallowing the ball at an altitude of 300 feet. Find the time,t, when the seagull ate the ball.

2)The ball described in problem #1 will reach its maximum height before being eaten by the seagull. After how many seconds will the ball reach its maximum height and what will that height be?



Above are the two problems I need help with. Since they all involve the same formula I hope its okay to post them together.I have the answers for both problems since these are just from a practice workbook but it doesnt explain how to get to these answers. For the first problem
I tried 300=-16t+160t but the result was extremely off:t+10t=300
I also tried using the vertex of a parabola formula: -160/2(-16)=128

For the second problem I had no idea where to start.
Thanks for reading/helping in advance. I am so terrible at math x.x

Let's help you be less terrible at math.

The symbols in math represent things. It frequently helps your thought process if you make sure you understand what each symbol represents.

What does f(t) represent? EDIT: I'll bet you dollars to doughnuts that the problem says f(t) rather than f(x)

What do you think - 16t + 160t represents?

 

[Bob Brown MSEE]

I would gladly pay you Tuesday for a doughnut today

What does f(t) represent? EDIT: I'll bet you dollars to doughnuts that the problem says f(t) rather than f(x)?

What does f(t) represent? EDIT: I'll bet you dollars to doughnuts that the problem says f(t) = -16t²+160t rather than f(x) = -16t²+160

 

[vanillah]

What does f(t) represent? EDIT: I'll bet you dollars to doughnuts that the problem says f(t) = -16t²+160t rather than f(x) = -16t²+160

Well you owe me! Heh. link:http://i880.photobucket.com/albums/ac9/sereda899/stuff/practiceproblems_zps6edd286a.png

I already know what you meant but how do I solve for t. I cant use the altitude of 300 anywhere and when I tried dividing by -16 the answers didnt match up. Anyway, I still need help with this problem.

 

[JeffM]

Well you owe me! Heh. link:http://i880.photobucket.com/albums/ac9/sereda899/stuff/practiceproblems_zps6edd286a.png

I already know what you meant but how do I solve for t. I cant use the altitude of 300 anywhere and when I tried dividing by -16 the answers didnt match up. Anyway, I still need help with this problem.

Did you read my post? That's post # 2. If so, why did you not answer the questions that I asked you to answer? If you want my help, please answer the questions posed.

You can use 300 somewhere, but not as you did. If you set up the proper eqation, you may if you choose divide both sides by 16, but it is unnecessary. I point out that you are unlikely to get a correct answer if you set up the wrong equation and then divide only one side of it by 16 as you did in your original post. Try responding to post # 2, and let's get you on the right path.

 

[Quaid]

f(x) = -16t^2 + 160

… where t is in seconds

You copied the function statement incorrectly. The term highlighted in red above is supposed to be 160t

Also, symbol x is a typographical error in your practice workbook. The symbol for the output must be f(t) because symbol t is used for the function's input (time).

The given model is not very good, anyway. The ball is hit at t = 0, and f(0) = 0. In other words, this model tells us that the batter hit the ball while it was on the ground, causing the ball to go straight up into the air. That's impossible.

A seagull … [swallows] the ball at an altitude of 300 feet.

The ball is 300 feet above the ground at two different times (going up and coming down). Exercise (1) ought to specify whether the ball is eaten on its way up or its way down.

As written, you need to read exercise (2) before attempting exercise (1). This also is not good. Maybe, you need to find a better practice workbook.

For the first problem I tried

300 = -16t + 160t

Substituting 300 for f(t) is the way to go, but, again, you incorrectly copied the function statement. The term in red above is supposed to be -16t^2

Solve the quadratic equation -16t^2 + 160t = 300

You will get two values for t. Pick the value corresponding to when the ball is on its way down.

I also tried using the vertex of a parabola formula: -160/(2(-16)) = 128

That's not appropriate for exercise (1) because we're not told that the seagull eats the ball at the ball's highest point.

However, you may use the vertex formula to answer exercise (2).

Don't forget to include the grouping symbols (shown above in red), and check your arithmetic. 128 is not correct.

If you need more help, please continue showing your work. Cheers :cool: