Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

A gun is fired upward from the ledge of a 176 foot cliff. The bullet leaves the gun with a velocity of 80 feet per second. If its height $h$ measured in feet is given in terms of time $t,$ measured in seconds by the equation $h=-16 t^{2}+80 t+176,$ determine (a) how high the bullet will go and how long it takes to reach that height, (b) how long does it take for the bullet to come back to the ground?

$$\text { (a) } 276 \mathrm{ft}, 2.5 \mathrm{sec}(\mathrm{b}) 6.65 \mathrm{sec}$$

Algebra

Chapter 1

Functions and their Applications

Section 4

Quadratic Functions - Parabolas

Functions

Missouri State University

University of Michigan - Ann Arbor

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

03:18

02:03

Firing an $M-16 .$ If an M…

03:41

If a projectile is shot ve…

01:48

A bullet is fired straight…

01:11

The height of a projectile…

03:01

Projectile If the initial …

01:29

03:06

Projectile The height in f…

02:08

Height of a Projectile A p…

So we're given this equation name of 16 t squared plus a T T plus 176. So there's two questions we have to answer. I guess there's actually three is understanding when we get to the maximum height, which is basically find the Vertex without knowing the calculus. And then when do we hit the ground? Which is basically what are the X intercepts? So the two processes are a little bit different. To find the Vertex, you first find the X value, which is negative. B over two A. So that's negative. 80 over doubling negative 16. So negative 80 divided by negative 32. I believe it comes out to exactly 2.5 seconds. So that's part of your first answer. You circle that? So now what you need to do is plug in 2.5 and for those t values, and that will tell you how high the object is at that moment. So as you type away, just make sure you do parentheses. You have to square before multiplying in a lot of students and do that wrong. You get an answer of 276 ft. Um, So those are your two answers for part A. Uh And then the third part is when it hits the ground the X intercepts. That's just the quadratic formula. So the quadratic formula tells you to do negative. Be negative. 80 plus or minus the square root of B squared minus four A. C. He's 176 all over to a two times in 8 16. Uh, so just as a heads up as you go to type this in your calculator, uh, you'll get a second answer because there would have been an X intercept over here. But ignore that answer because they don't care about the negative value for the time solving for T in this problem, T equals so as you type it away and you get the correct answer. Uh, for a letter, B is 6.65 seconds and there's your three answers. Shit.

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:20

A barnyard is to be fenced is as indicated in Figure $22 .$ If 6000 feet of …

a) sketch the graph of the given function, and then draw the tangent line at…

02:31

In each of the following exercises, solve the given inequality.$$x^{2}-4…

01:09

Use the zeros, vertical and horizontal asymptotes along with the sign of the…

01:14

In each of the following, solve the given quadratic equation exactly using t…

02:01

Find the equations of two lines parallel to $x=2$, and 6 units from it.

02:36

Sketch the graph of $\frac{(x-1)^{2}}{4}+\frac{(y+2)^{2}}{9}=1$

02:50

Solve each of the quadratics by first completing the square. When the roots …

03:22

Determine whether the given equations is a circle, a point, or a contradicti…

01:10

Determine if the function defined by the given equation is odd, even or neit…