# Thread: Derivatives - Falling Objects

1. ## Derivatives - Falling Objects

I have to answer a problem using the following function:

-16t^2 + Vot + So

(Sorry the notation is bad, but the middle term is initial velocity and So is distance)

The question: A ball is thrown straight down from the top of a 220ft building with an initial velocity of -22 feet per second. What is its velocity after 3 seconds? What is its velocity after falling 108 feet?

I can get the first part of the problem. I found the derivative to be V=-32t-22, so i plugged in 3 and got -118ft/s, easy enough.

However, I don't know how to find the velocity after 108 feet. I remember I'm supposed to say that the ball is 112 feet from the ground instead of saying it fell 108 feet, but whenever I try to solve it seems like I have too many unknown variables. Any hints?

2. Originally Posted by vesperka
I have to answer a problem using the following function:

-16t^2 + Vot + So

(Sorry the notation is bad, but the middle term is initial velocity and So is distance)

The question: A ball is thrown straight down from the top of a 220ft building with an initial velocity of -22 feet per second. What is its velocity after 3 seconds? What is its velocity after falling 108 feet?

I can get the first part of the problem. I found the derivative to be V=-32t-22, so i plugged in 3 and got -118ft/s, easy enough.

However, I don't know how to find the velocity after 108 feet. I remember I'm supposed to say that the ball is 112 feet from the ground instead of saying it fell 108 feet, but whenever I try to solve it seems like I have too many unknown variables. Any hints?
okay, so your position function here is:

$s(t) = -16t^2 - 22t + 220$

now, to find the velocity after it falls 108 ft, that is, it is 112 ft off the ground, we need to find the time when the ball it at this height and then plug that into the velocity function--which you already found. thus we must solve

$112 = -16t^2 - 22t + 220$

for $t$

and then plug that $t$ into $v(t)$

3. Alright, I found t=1.197 seconds, giving me a velocity of -60.312 ft/s. Thanks

I was doing it wrong before because I was solving -112 = -16t^2 + 22t + 108. I had the right idea but I wasn't quite using the formula properly