I need to know if there is a standard method of finding the answer to this. My exam is tomorrow and my teacher gave us a set of topics to study. This is titled Projectile Motion!
The question is:
The function h=-5t^2 + 20t + 2 gives the approximate height, h meters of a trown football as a function of the time, t seconds since it was thrown. The ball hit the ground before the receiver could get near it.
a) How long was the ball in the air, to the nearest tenth of a second?
b) for how many seconds was the height of the ball at least 17 m?
The answers are:
I dont understand how to get the answers though. Sorry if there are misspelling in the question i had to rewrite it from the text book. Thanks again!
Remember that in , h stands for the height. When the ball hits the ground, the height is 0, so plug that in for h. This gives:
Now, solve that by the quadratic equation to figure out what t equals when h is zero.
Similarly, you can find out the two times the ball was at a height of 17m by plugging in 17m for h:
Move the 17 to the other side, then solve by factoring / quadratic equation. You'll get two times. The ball was ABOVE 17m between those two times, so you can find the length of time simply by subtracting.
See how that goes!
Thank you soo much! I have not tried it yet, im just about too! Thanks soo much! I will post my answer soon.
Edit: Something is wronge. Im not sure what though but ill start with the first one.
When i sub 0 it doesn't make a difference and when i do the quadratic formula i get -4 and 8 which is not the answer.
For the second one i subed 17. Here are my steps:
17 = -5t^2 + 20t + 2
0 = -5t^2 + 20t - 15
and i end up with -1 and 3! What am i doing wrong?
Alright i've updated the thread since the new answer wont work! Please read previuse updated post.
Thanks guys! You where right i was doing my quadratic equation wronge (I include the square root in the calculation to save time) But just to make sure. Whenever i get a question like this i just factor or do a quadratic formula and I have my answer? Thanks again you've all been a great help!