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The equation h = -16t^2 + 40t models the altitude a football will reach t seconds after it is kicked.

Apr 14, 2020

#1
+27
+1

Hello, Friend!

For this equation, the easiest way to do it is to plug in different times. Let's start!

First off, it'll probably take a second for the football to get near it's peak, so let's start with t=1.

h=-16(1)+40(1) 2 => h=-16+40 => h=24

Ok, not quite 25. Let's try t=1.25!

h=-16(1.25) 2+40(1.25) => h=-25+50 => h=25

Great! We found the answer to A - the ball reaches 25 feet after 1.25 seconds. But does it keep rising enough to hit 30 feet, or will it plateau too soon? Let's try t=1.5.

h=-16(1.5) 2+40(1.5) => h=-36+60 => h=24

As it turns out, the ball has reached it's plateau and rises no higher! In the end, we find that the answer is yes, just barely, for A but a resounding no for B.

I hope this helped you get a firmer understanding of this kind of equation! Physics seems hard now, but you'll look back soon enough and say, "That was actually kinda fun!" Good luck on your journey, my friend!

Apr 14, 2020
#2
+12213
+2

The equation h = -16t^2 + 40t models the altitude a football will reach t seconds after it is kicked.

Apr 14, 2020
#3
+27
+1

While this does get you there eventually, it's much longer and harder than is really necessary. You could also use matrices, but it also is much more time-consuming and more complex than is really necessary. If you have a feel for about how high you can get with those kinds of numbers, you can easily poke around that area until you find the peak and get the answer much quicker.

Daewei  Apr 14, 2020