Easy Quadratic Projectile Word Problem

Easy Quadratic Projectile Word Problem

Postby Guest » Thu Mar 07, 2019 1:41 pm

Hey, I just made an account here and I submitted my first post due to me needing immediate assistance with a homework question. Although my post has been on awaiting review for 25minutes now, when I need it now. I just started a new unit today and I didn't really understand anything and of course I was assigned homework, do you think you could answer this question with steps so I know how to do it for next time? Would be great.

"A quarterback throws a football. The height, h metres, of the ball is given by the equation h = - 5t^2 + 20t + 2 where t is the time in seconds after the ball is thrown.

c) What is the height of the ball 1 second after it is thrown?
d) What is the maximum height of the ball?
e) How long does it take for the ball to reach the maximum height?
f) For how long is the ball more than 10 m above the ground?"
Guest
 

Re: Easy Quadratic Projectile Word Problem

Postby HallsofIvy » Thu Mar 07, 2019 7:12 pm

Guest wrote:Hey, I just made an account here and I submitted my first post due to me needing immediate assistance with a homework question. Although my post has been on awaiting review for 25minutes now, when I need it now. I just started a new unit today and I didn't really understand anything and of course I was assigned homework, do you think you could answer this question with steps so I know how to do it for next time? Would be great.

"A quarterback throws a football. The height, h metres, of the ball is given by the equation h = - 5t^2 + 20t + 2 where t is the time in seconds after the ball is thrown.

c) What is the height of the ball 1 second after it is thrown?

"The height, h metres, of the ball is given by the equation h = - 5t^2 + 20t + 2 where t is the time in seconds after the ball is thrown."
So when t= 1 sec., h= -5(1)^2+ 20(1)+ 2 meters. What is that?

d) What is the maximum height of the ball?

"Complete the square"! -5t^2+ 20t+ 2= -5(t^2- 4t)+ 2. You should know that "(t- a)^2= t^2- 2at+ a^2" so that, in particular, (t- 2)= t^2- 4t+ 4. We can make that "t^2- 4t" a "perfect square" by adding (and subtracting) 4. -5t^2+ 20t+ 2= -5(t^2- 4t+ 4- 4)+ 2= -5(t- 2)^2+ 22. I hope you know that a square is never 0 so that is 22 minus something. It will be 22 when that "t- 2" is 0. For any other value of t, it is less.

e) How long does it take for the ball to reach the maximum height?

You know the maximum height from (d). What is t at that point?

f) For how long is the ball more than 10 m above the ground?"

The height of the ball will be 10 m when -5t^+ 20t+ 2= 10. That has two solutions. What are they? When is h larger than 10?

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