Problem

The displacement (in meters) of a particle moving…

View

Question

Answered step-by-step

Problem 14 Medium Difficulty

If a rock is thrown upward on the planet Mars with a velocity of $ 10 m/s $, its height (in meters) after $ t $ seconds is given by $ H = 10t - 1.86t^2 $.

(a) Find the velocity of the rock after one second.
(b) Find the velocity of the rock when $ t = a $.
(c) When will the rock hit the surface?
(d) With what velocity will the rock hit the surface?

Video Answer

Solved by verified expert

Textbook Answer

Official textbook answer

Video by Mary Wakumoto

Numerade Educator

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

October 27, 2020

That was not easy, glad this was able to help

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 2

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

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Video Transcript

Alright so here we are on mars we throw up An object with the starting velocity of 10 m/s and we observed that our height with time is 10 t minus 1.86 T squared. And we're going to find out a whole bunch of different features regarding this um this motion. Okay so part A. We just want to find V. F. T. And V. F. T. Is just the derivative of our position ah equation. So we will use the power rule and get 10 -3.72 T. Using power rules. So that's just doing power role on both parts. Um we need to also find v. of one by the way we have some units I believe. Yes our unit will be meters per second. Once I plug in the number. So if if we want to know the velocity at one second, one second after it was launched then we would just plug in one for the T. So times one and we end up with 6.28 meters per second. So the velocity one second later Is eight, sorry 6.28 m/s. Alright, let's see the next thing we need to do now we need to just in general what is the for any time A. So that will give us 10 -3.72 a. That's just plugging in a 14. Alright, that was pretty easy. Okay, Part C. Part C is now the rock is gonna hit the surface and we want to find the time it takes. So we basically want to find out when this um the rocks that's a rock was thrown. And so when the rock um Uh is back down to zero So that would be down to zero m. So We can solve this by pulling out A. T. that gives me 10 -1.86 T. T. Times 10 minus 1.8 62 B. Zero either T. Is zero. Well that's the starting time or 10 -1.860 equals zero. Which comes out to be T equals 10 over 1.86. And that is 5.376 seconds. So that's the time we want the time that the rock hits back to mars Alright one more part to go party and part D. We just want the velocity when the rock hits the ground. So we're going to go ahead and plug in our time. And into the velocity equation which was 10 -3.72 times that time. And when it's like that in To our calculator we get -10 m/s. So just like on earth if I launched from ground level when it finally the rock returns, this is without any air resistance. When the rock returns it returns with the same speed but in the opposite direction which is then downwards. So anyway hopefully that helps have a wonderful day

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.

Problem

The displacement (in meters) of a particle moving…

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

More Answers

Related Courses

Calculus: Early Transcendentals

Related Topics

Discussion

Top Calculus 1 / AB Educators

Grace He

Kayleah Tsai

Kristen Karbon

Michael Jacobsen

Calculus 1 / AB Courses

Recommended Videos

Watch More Solved Questions in Chapter 2

Video Transcript

James Stewart

Calculus: Early Transcendentals

Grace He

Kayleah Tsai

Kristen Karbon

Michael Jacobsen

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

Calculus: Early Transcendentals

Grace He

Kayleah Tsai

Kristen Karbon

Michael Jacobsen

James StewartCalculus: Early Transcendentals

Grace He

Kayleah Tsai

Kristen Karbon

Michael Jacobsen

James Stewart

Calculus: Early Transcendentals