Elias hits a baseball into the air. the equation h=-16t^2+60t+3 models the height h in feet of the balls after t seconds. how long is the ball in the air?

Question

Nicoley269 · Answer

@Hero please help?

Hero · Answer

$h$ represents the height of the ball after $t$ seconds. We know that the ball will basically fly into the air reach a maximum height then fall to the ground. So when the question asks "how long has the ball been in the air" that implies that the ball has already hit the ground. When the ball hits the ground, its height will be zero. So if we set $h = 0$ we can solve for $t$.

Hero · Answer

In other words, we have to solve the equation $0 = -16t^2 + 60t + 3$ for $t$.

Nicoley269 · Answer

ok. i did that, should i use the quadratic formula?

Hero · Answer

Yes, that is one valid way to solve for $t$.

Hero · Answer

Me personally though, I don't like using the quadratic formula. Would rather solve algebraically.

Nicoley269 · Answer

whats the other way?

Nicoley269 · Answer

how?

Hero · Answer

It's a bit involved. You should probably stick to the quadratic formula. It's the fastest way to solve for it by hand without using a calculator.

Nicoley269 · Answer

ok

Nicoley269 · Answer

|dw:1526185492114:dw|

Hero · Answer

|dw:1526185806722:dw|

Nicoley269 · Answer

oh yea! oops

Nicoley269 · Answer

|dw:1526185866661:dw|

Hero · Answer

|dw:1526185980161:dw|

Nicoley269 · Answer

|dw:1526186039191:dw|

Hero · Answer

At this point , it would be best to split it into two equations.

Nicoley269 · Answer

how could i do that?

Hero · Answer

$\dfrac{-60 + \sqrt{3792}}{-32}$

$\dfrac{-60 - \sqrt{3792}}{-32}$

Nicoley269 · Answer

ok, but 3792 cant be square rooted

Hero · Answer

And only the positive result will matter because height can't be negative. It can be rooted approximately. Use a calculator.

Nicoley269 · Answer

i dont have a calculator that has roots or square.

Hero · Answer

What kind of calculator are you using currently?

Nicoley269 · Answer

ipad

Hero · Answer

Can you screenshot the calculator you're using? I'd like to see it.

Nicoley269 · Answer

im using a computer for this problem so i cant screen shot and post it.

Hero · Answer

What is the name of the calculator app you're using?

Nicoley269 · Answer

on a different calculator app, i got -0.049 and 3.799

Nicoley269 · Answer

it just says calculator

Hero · Answer

So which result is the positive result?

Nicoley269 · Answer

3.799

Hero · Answer

So what you do is write $t \approx 4$. Then write "The ball is in the air for approximately 4 seconds.\)

Nicoley269 · Answer

ok. thank you so much!