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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?"
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Easy Quadratic Projectile Word Problem
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Re: Easy Quadratic Projectile Word Problem
by Guest » Tue Jun 15, 2021 8:39 am
You are told that "the height of the ball, in metres, of a ball is givien by the equation $h= -5t^2+ 20t+ 2$ where t is the time in seconds after the ball is thrown".
The first question is "c) What is the height of the ball one second after it is thrown?"
Since this is "c" I asssume you were able to do "a" and "b". But you weren't able to do this? Do you understand that it is telling you that t= 1 and asking you to calculate $h= -5t^2+ 20t+ 2= -5(1^2)+ 20(1)+ 2$? That's an easy calcultion! Don't forget that the answer is in metres.
d) What is the maximum height ot the ball? Complete the square! $-5t^2+ 20t+ 2= -5(t^2- 4t)+ 2$. What do you need to add to $t^2_ 4t$ to make it a perfect square? That is, you want $(t- a)^2= t^2- 2at+ a^2$. Here, you want 2a= 4, So what is a? Then what is $a^2$? You need to both add and subtract that $a^2$ to get $-5(t- a)^2+ 5a^2+ 2$. Since a square is never negative, that is always $5a^2+ 2$ minus something. So the maximum is $5a^2+ 2$ at t= a. What is a?
e) How long does it take for the ball ti reach its maximum height? What was t= a in (d)?
f) For how long is the ball more than 10 metres above the ground? The ball will pass 10 metres on its way up then again on its way down. Both of those times satisfy $-5t^2+ 20t+ 2= 10$ or $-5t^2+ 20t- 8= 0$. That is a quadratic equation so has two solutions What are the solutions to that equation?
The first question is "c) What is the height of the ball one second after it is thrown?"
Since this is "c" I asssume you were able to do "a" and "b". But you weren't able to do this? Do you understand that it is telling you that t= 1 and asking you to calculate $h= -5t^2+ 20t+ 2= -5(1^2)+ 20(1)+ 2$? That's an easy calcultion! Don't forget that the answer is in metres.
d) What is the maximum height ot the ball? Complete the square! $-5t^2+ 20t+ 2= -5(t^2- 4t)+ 2$. What do you need to add to $t^2_ 4t$ to make it a perfect square? That is, you want $(t- a)^2= t^2- 2at+ a^2$. Here, you want 2a= 4, So what is a? Then what is $a^2$? You need to both add and subtract that $a^2$ to get $-5(t- a)^2+ 5a^2+ 2$. Since a square is never negative, that is always $5a^2+ 2$ minus something. So the maximum is $5a^2+ 2$ at t= a. What is a?
e) How long does it take for the ball ti reach its maximum height? What was t= a in (d)?
f) For how long is the ball more than 10 metres above the ground? The ball will pass 10 metres on its way up then again on its way down. Both of those times satisfy $-5t^2+ 20t+ 2= 10$ or $-5t^2+ 20t- 8= 0$. That is a quadratic equation so has two solutions What are the solutions to that equation?
- Guest
Re: Easy Quadratic Projectile Word Problem
by Guest » Tue Nov 09, 2021 11:20 am
Thank you very much!
- Guest
Re: Easy Quadratic Projectile Word Problem
by sueambrose121 » Mon Dec 27, 2021 3:12 pm
Wow thanks a lot.
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