1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
SpyIntel [72]
2 years ago
11

A ball is thrown into the air with initial velocity v(0) = 3i + 8k. The acceleration is given by

Mathematics
1 answer:
Paladinen [302]2 years ago
8 0

Use the fundamental theorem of calculus to find the velocity and position functions.

\displaystyle \mathbf v(t) = \mathbf v(0) + \int_0^t \mathbf a(u) \, du \\\\ ~~~~ = (3\,\mathbf i + 8\,\mathbf k) + (8\,\mathbf j - 16\,\mathbf k) \int_0^t du \\\\ ~~~~ = 3\,\mathbf i + 8t\,\mathbf j + (8-16t)\,\mathbf k

Take the starting position of the ball to be the origin, so \mathbf r(0)=\mathbf 0.

\displaystyle \mathbf r(t) = \mathbf r(0) + \int_0^t \mathbf v(u) \, du \\\\ ~~~~ = \int_0^t \bigg(3\,\mathbf i + 8u\,\mathbf j + (8-16u)\,\mathbf k\bigg) \, du \\\\ ~~~~ = 3t\,\mathbf i + 4t^2\,\mathbf j + (8t - 8t^2)\,\mathbf k

Compute the ball's position vector at t=1.

\mathbf r(1) = 3\,\mathbf i + 4\,\mathbf j

The distance from the ball's starting location at \mathbf r(0) to \mathbf r(1) is then

\|\mathbf r(1) - \mathbf r(0)\| = \|3\,\mathbf i + 4\,\mathbf j\| = \sqrt{3^2 + 4^2} = \boxed{5}

You might be interested in
Pls help me with this proof! I only have a short amount of time
Anna35 [415]
Because it is in the middle of those given points
7 0
3 years ago
D2-9k+3 for d=10 and k=9
AVprozaik [17]

Answer:

22

Step-by-step explanation:

10^2-9(9)+3

100-81+3

19+3

22

8 0
3 years ago
the atlanta braves are offering bobblehead to every 10th person who enters your fundraiser. the nashville predators are offering
Paha777 [63]

In this situation, attendee number thirty will be the first one o receive both the bobblehead and the ticket.

<h3>Which attendees will receive the bobblehead and the ticket?</h3>

Bobblehead:

  • Attendee number 10
  • Attendee number 20
  • Attendee number 30

Ticket:

  • Attendee number 15
  • Attendee number 30

<h3>What can be concluded?</h3>

It can be concluded the attendee number 30 will be the first one to receive both the ticket and the bobblehead.

Learn more about ticket in: brainly.com/question/14001767

#SPJ1

6 0
2 years ago
Seven of the Apple computers have specialized movie editing software. Approximately what percent of the Apple computers can be u
kodGreya [7K]

If there are 30 Apple computers and 7 of the computers have a specialized movie editing software, then that would be 23.3333333% of the Apple computers can be used for editing movies.

7/30x100= 700/30

700/30= 23.33%

5 0
3 years ago
What is the relationship between the x and y values on #2?
Ghella [55]
For y u add 2 and x add one
8 0
3 years ago
Other questions:
  • HELPPPP ASAP !!!!!!!!!
    15·2 answers
  • Suzanne bought 50 apples at the apple orchard. She bought 4 times as many red apples as green apples. How many more red apples t
    11·1 answer
  • Unit rate for 3 ounces for every 3/4 cup
    10·1 answer
  • 6.- Find the area under the standard normal distribution: to the left of z=-1.55.
    13·1 answer
  • |-2y+6|=6 please show the steps involved!!!
    8·2 answers
  • M∠1 = _°<br><br> a) 140<br> b) 160<br> c) 80
    6·2 answers
  • What is the slope of the line that passes through the points listed in the table?
    11·2 answers
  • Solve this question <br>a=7+3​
    7·2 answers
  • How do I fine the perimeter of these triangles?
    15·1 answer
  • What is the value of x?
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!