The height of a ball is thrown directly upward from an initial height of $160$ ft with an initial velocity of $48$ ft per second is given by the function:

$s(t) = -16t^2 + 48t + 160$, where $s(t)$ gives the ball's height above ground in feet, $t$ seconds after it is thrown. How long will it take for the ball to hit the ground?

  • 2
    $\begingroup$ What are your thoughts on the problem? $\endgroup$ – Peter Woolfitt Jul 8 '14 at 5:28
  • $\begingroup$ I need help in trying to solve it. I do not know where to start. Do I start by factoring it out? $\endgroup$ – thes4s Jul 8 '14 at 5:30
  • $\begingroup$ Divide it all by 16, and try to factorise it then. It comes out nicely. $\endgroup$ – user105475 Jul 8 '14 at 5:30
  • $\begingroup$ When the ball hits the ground $s(t)=0$. How do you solve such kind of equations? $\endgroup$ – Hassan Muhammad Jul 8 '14 at 5:32
  • $\begingroup$ So it becomes s(t) = -t^2 + 3t + 10 $\endgroup$ – thes4s Jul 8 '14 at 5:32


You have a quadratic so, if you factor it and you will find the roots or in other words, when the balls hits the ground.

HINT $2$

You can factorize your polynomial by dividing by $-16$ and finding two numbers which add to $-3$ and multiply to $-10$

HINT $3$

Your answer should be in the form $-16(x-a)(x+b)$ where $a$ and $b$ are the numbers which make your equation zero or in other words, the roots.

  • $\begingroup$ I divided it by 16. and got s(t)= -t^2+3t+10. Then I factored it and got (-t-2)(t-5) so the answer is 5 correct? $\endgroup$ – thes4s Jul 8 '14 at 5:37
  • $\begingroup$ You should also take out the negative sign from $s(t)$ and you will get a similar answer: $-16(t+5)(t-2)$ $\endgroup$ – Jeel Shah Jul 8 '14 at 5:42
  • $\begingroup$ I understand it now. thank you! $\endgroup$ – thes4s Jul 8 '14 at 5:45
  • 1
    $\begingroup$ @gekkostate It should be $-16(t-5)(t+2)$. $\endgroup$ – Peter Woolfitt Jul 8 '14 at 5:47
  • $\begingroup$ Anytime! I'm not sure if you have visited the help center or seen the FAQ but if you notice, there is a small check mark beside this answer and any other answer you will see on this website. There is also an upvote button and a downvote button. When you have 15 rep, you can upvote and downvote an answer. Also, if you hit the checkmark then the answer will be accepted and will close a "loop" so to speak. $\endgroup$ – Jeel Shah Jul 8 '14 at 5:48

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.