Download the App!

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

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Problem

If a ball is thrown vertically upward with a velo…

03:24

Question

Answered step-by-step

Problem 7 Hard Difficulty

The height (in meters) of a projectile shot vertically upward from a point $2 \mathrm{~m}$ above ground level with an initial velocity of $24.5 \mathrm{~m} / \mathrm{s}$ is $h=2+24.5 t-4.9 t^{2}$ after $t$ seconds.
(a) Find the velocity after $2 \mathrm{~s}$ and after $4 \mathrm{~s}$.
(b) When does the projectile reach its maximum height?
(c) What is the maximum height?
(d) When does it hit the ground?
(e) With what velocity does it hit the ground?


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

Heather Zimmers
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Heather Zimmers

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

More Answers

03:27

Amrita Bhasin

Related Courses

Calculus 1 / AB

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 7

Rates of Change in the Natural and Social Sciences

Related Topics

Derivatives

Differentiation

Discussion

You must be signed in to discuss.
Top Calculus 1 / AB Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

01:44

A projectile is fired vert…

0:00

If a ball is thrown vertic…

03:53

A ball is thrown upward, a…

01:47

Flight of a projectile An …

03:14

A projectile is launched a…

07:14

A projectile is launched f…

01:07

The height of a projectile…

Watch More Solved Questions in Chapter 3

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39

Video Transcript

All right, So we're given the equation for the height ever projectile, and we want to start by finding the velocity after two seconds and four seconds. And so we're going to find the velocity in General V of tea by finding the derivative of the height function. So the derivative would be 24.5 minus 9.8 t Now, to find the velocity it to weaken substitute to in there. So we have 24.5 minus 9.8 times two, and that gives us 4.9 and the units would be meters per second and the velocity at time four will just substitute a four in there and we get negative 14.7 meters per second for part B. We want to find the time when the projectile reaches its maximum height and we have two ways to do this. One way is sort of an algebra two way. We recognize that this is a parabola and it opens down and we could find the Vertex and the X coordinate of the Vertex would be the time. The other way is a calculus way. And we would realize that the velocity would be zero at the time when it's at its maximum point, because we would have a horizontal tangent line there. And so I say we do the calculus way since we're in calculus. So we want the velocity equals zero. So we take our velocity 24.5 minus 9.80 and said it equal to zero. And we saw for teeth. So we have 9.8 t equals 24.5 and we end up with t equals 2.5 seconds. So that is the time when the projectile is at the maximum height for part C. We're finding the maximum height. So we're going to take the time we just found, which was 2.5 seconds and substituted into our height equation and will compute this and we end up with 32.6 to 5 meters for part D. We want to find the time when it hits the ground. So when it hits the ground, its height is zero. So we're going back to the height equation on. We're setting it equal to zero. I'm going to rearrange the terms of little bits. We have negative 4.9 t squared plus 24.5 t plus two equals zero. Now, unfortunately, this is not factory ble. So we're going to solve this equation with the quadratic formula, and I'm going to start by multiplying the whole equation by negative one just so that we can lead with a positive coefficient. Just seems to make life a little bit easier. Now, we're going to use the quadratic formula so we have t equals the opposite of B over two, a plus or minus the square root of B squared minus four a. C all over two a. And you're gonna simplify that and work that out and we end up with 2.5 plus or minus the square root of 6 39.45 over 9.8 and you're gonna put that in your calculator and you get to answers approximately 5.8 or negative 0.8 But you realize that you're not going to keep the negative time in this context. So just the positive one now, because for party, we're going to use this number for something else. We might store that in our calculators, so that we will be more accurate for part e for party were finding the velocity when it hits the ground and we use our velocity equation and we substitute that number we just got in the previous part the approximate values 5.0, wait. It would be a good idea to use the stored value so you don't lose too much accuracy. So we have 24.5, minus 9.8 times five point a 5.0.8 and we end up with approximately negative 25.3 meters per second.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
142
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
68
Hosted by: Alonso M
See More

Related Topics

Derivatives

Differentiation

Top Calculus 1 / AB Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Caleb Elmore

Baylor University

Kristen Karbon

University of Michigan - Ann Arbor

Calculus 1 / AB Courses

Lectures

Video Thumbnail

04:40

Derivatives - Intro

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

Video Thumbnail

44:57

Differentiation Rules - Overview

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

Join Course
Recommended Videos

01:44

A projectile is fired vertically upward with an initial velocity of $49 \mathrm…

0:00

If a ball is thrown vertically upward with a velocity of $24.5 \mathrm{~m} / \m…

03:53

A ball is thrown upward, and its height, $h,$ in metres above the ground after …

01:47

Flight of a projectile An object is projected vertically upward with an initial…

03:14

A projectile is launched at $t=0$ with initial speed $v_{\mathrm{i}}$ at an ang…

07:14

A projectile is launched from the ground with an initial speed of 200 ft/ sec a…

01:07

The height of a projectile shot from ground level is given by $s=-16 t^{2}+256 …
Additional Mathematics Questions

01:47

the rate ow mirror of length 20 cm and width 15 cm is tobe framed with a 2 c…

00:45

A farmer wants to find out the average number of apples produced by the appl…

01:07

Search results for In a fraction, if numerator is increased by 15% and denom…

02:11

A family went to a hotel and spent Rs.350 for food and paid extra 5% as GST.…

02:46

simplify 5^n + 4 - 6 x 5^n + 3 / 9 x 5^n + 2 - 2^2 x 5^n - 1

03:12

Find the distance between lines 2x+3y -5 =0 and 6x + 9y – 5 =0

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started