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
Simora [160]
3 years ago
13

Question

Mathematics
2 answers:
IgorLugansk [536]3 years ago
7 0

Answer:

the time is 1.57 sec and the distance is 49.32mm

Step-by-step explanation:

Given that,

The angle is 180°

Angular velocity is 2rev/sec

The radius is 10mm

we are to find the time and distance traveled at that time

The formula is

θ = at

where t is the time,

a is the angular velocity

θ is angle in radian

so,

θ = 180° × π/180°

θ = π

= 3.14

Hence ,

θ = at

3.14 = 2t

t = 1.57sec

let the distance be xmm

\frac{1.57 \times 180^0}{360} = \frac{x}{20 \pi} \\\\0.785 = \frac{x}{20 \pi} \\\\x = 49.32mm

Therefore , the time is 1.57 sec and the distance is 49.32mm

Vlad [161]3 years ago
6 0

Answer:

a) 0.25 s

b) 15.71 mm

Step-by-step explanation:

Given:-

- The radius of the coin, r = 10 mm

- The angle swept by the coin, θ = 180°

- The frequency of ration of the coin, f = 2 rev /s

Find:-

How long will it take the coin to roll through the given angle measure at the

given angular velocity?

How far will it travel in that time?

Solution:-

- We will first determine the angular speed ( ω ) of the coin. That is the rate of change of angle swept. Mathematically expressed as:

                       ω = dθ / dt = 2*π*f

- Separate the variables:

                      dθ = 2*π*f . dt

- Integrate both sides.

                      ∫dθ = 2*π*f ∫ dt

                      θ = 2*π*f*t

- The time taken to sweep an angle of ( θ ) is:

                      t = θ / 2*π*f

Where, θ is in radians. 180° = π radians

- Plug in the values:

                     

                      t = π / 2*π*( 2 )

                      t = 1 / 4 = 0.25 s   ... Answer

- The tangential speed (v) of any point on the circumference of a coin is. Considering only rolling motion of the coin:

                    v = r*ω = 2*r*π*f

- The velocity of the any point on the rolling coin circumference would be:

                   v = 2*(10)*π*(2)

                  v = 40π mm/s

- Since we are considering the coin as a rigid body and not a point mass. We have to determine the velocity of the center of mass of the coin ( Vcm ).

- Consider a coin as a circle. The point of contact of the between the circle ( coin ) is called the center of instantaneous velocity.

- Then mark two horizontal velocity vectors. One starts at the center of mass of the coin ( pointing right ): Denote this as the velocity of center of mass ( Vcm ).

- Other one starts from top most point lying on the circumference of the circle, this vector should be longer than the one made at center of mass (pointing right ): Denote this as the tangential velocity ( v ).

- Now joint the heads of two vectors ( v and Vcm ) with the center of instantaneous velocity ( contact between coin and surface ). Now make a vertical line that starts the top most point passing through center of mass and ends at the center of instantaneous velocity.

- We will end up with two similar triangles. We will use the law of similar triangle and determine the velocity of center of mass ( Vcm ):

                       2r / r = v / Vcm

                       Vcm = v / 2

-  Evaluate the velocity of center of mass ( Vcm ):

                      Vcm = 40π / 2

                      Vcm = 20π  mm/s    

- Use the distance-speed-time relationship and determine how far the coin travelled ( s ) in the computed time in part a:

                      s = Vcm*t

                      s = 20π*0.25

                      s = 5π = 15.70796 mm

Answer: The distance travelled by the coin in the time interval of 0.25 seconds is 15.71 mm ( rounded to nearest tenth )

You might be interested in
PLEASE HELP
Assoli18 [71]

Simplest form I can do

5 0
3 years ago
I don’t understand number 5
yarga [219]
Multiply what’s on the outside to the inside, the variable is always a lower case letter such as x,
4 0
3 years ago
Select the inequality that match the situation:
elena55 [62]

Answer:

Each student club must contribute $ 33.33 in order to meet the fundraising goal.

Step-by-step explanation:

Given that a school fundraiser has a minimum target of $ 500. Faculty have donated $ 100 and there are 12 student clubs that are participating with different activities, to determine how much money should each club raise to meet the fundraising goal, the following calculation must be performed:

(500 - 100) / 12 = X

400/12 = X

33,333 = X

Thus, each student club must contribute $ 33.33 in order to meet the fundraising goal.

7 0
3 years ago
a truck rental company charges $19.95 to rent a truck plus $0.24 per mile driven. Find the cost to rent a truck and drive 188 mi
zubka84 [21]

Answer:

$65.07

Step-by-step explanation:

We know in this problem they charge a $19.95 fee plus the total number of miles.

0.24 times 188 = 42.12 that´s only for the miles then the rental fee

42.12 + 19.95= 65.07

4 0
3 years ago
Cho tam giác ABC vuông tại C, biết : Góc A = 50 độ. Tính góc B
chubhunter [2.5K]

Answer:

Tổng 3 góc trong 1 tam giác là 180 độ

Vậy góc B = 180 - A - C = 180 - 90 - 50 = 40 độ

8 0
2 years ago
Read 2 more answers
Other questions:
  • An 8 inch by 6 inch rectangle is the base of the rectangular prism below. What is the lateral area of the figure? 140 square inc
    11·2 answers
  • Can u plz help me with this question
    13·2 answers
  • If an item is 30% off and 350 how much is the original price
    15·1 answer
  • Please help with number 9 & 10
    8·1 answer
  • What’s the answer please someone ?
    9·1 answer
  • Micky spent 3 1/4 hours practicing his trumpet. He needs to spend 5 1/2 hours receive an A in band. How many hours does Mickey n
    6·1 answer
  • What is the total amount of paper glass and plastic waste generated
    11·1 answer
  • Find the area of this polygon and round to the tenth
    6·1 answer
  • Solve for x……………………….
    14·2 answers
  • As a single logarithm, 2log2 6- log29+ 1/3log2 27 = log2 12.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!