A typical running track is an oval with 74-m-diameter half circles at each end. a runner going once around the track covers a distance of 400 m . suppose a runner, moving at a constant speed, goes once around the track in 1 min 40 s. what is her centripetal acceleration during the turn at each end of the track?
Answer:
Her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]
Step-by-step explanation:
Total distance covered in one round , D= 400 m
Time taken to cover one round , T = 1 min 40 s = 100 sec
Speed of runner , [tex]V=\frac{D}{T}=\frac{400}{100}\, \frac{m}{s}= 4.0\, \frac{m}{s}[/tex]
Now centripetal acceleration is given by
[tex]a_c=\frac{V^{2}}{R}[/tex]
where [tex]V= 4.0\frac{m}{s}[/tex]
[tex]Radius, R= \frac{Diameter}{2}=\frac{74}{2}m=37\, m[/tex]
[tex]\therefore a_c=\frac{4^{2}}{37}\, \frac{m}{s^{2}}=0.432\, \frac{m}{s^{2}}[/tex]
Thus her centripetal acceleration during the turn at each end of the track is [tex]0.432\, \frac{m}{s^{2}}[/tex]
The centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
Explanation:
It is given that the diameter of oval track that consists of two half circles at each end is [tex]74{\text{ m}}[/tex] .
The distance runner runs once around the track is [tex]400{\text{ m}}[/tex] . The runner covers one round of track in [tex]1{\text{ m}}[/tex] and [tex]40{\text{ s}}[/tex] .
Our aim is obtain the value of centripetal acceleration for runner at each track.
The expression for centripetal acceleration is shown below.
[tex]{a_c}=\frac{{{v^2}}}{R}[/tex] …… (1)
Here, [tex]v[/tex] is the speed of the runner and [tex]R[/tex] is the radius of track.
The speed of the runner is the ratio of distance she takes to cover the track to the time taken by her.
The time in seconds is calculated as,
[tex]\begin{aligned}t&=60{\text{ s}}+40{\text{ s}}\\&=100{\text{ s}}\\\end{aligned}[/tex]
The distance covered is [tex]400{\text{ m}}[/tex] , so the speed calculated is shown below.
[tex]\begin{aligned}{\text{speed}}&=\frac{{{\text{distance}}}}{{{\text{time}}}}\\&=\frac{{400{\text{ m}}}}{{100{\text{ s}}}}\\&=4{\text{ }}{{\text{m}}\mathord{\left/{\vphantom {{\text{m}}{\text{s}}}}\right.\kern-\nulldelimiterspace}{\text{s}}}\\\end{aligned}[/tex]
The radius of track calculated is shown below.
[tex]\begin{aligned}R&=\frac{d}{2}\\&=\frac{{74{\text{ m}}}}{2}\\&=37{\text{ m}}\\\end{aligned}[/tex]
Substitute [tex]4[/tex] for [tex]v[/tex] and [tex]37[/tex] for [tex]R[/tex] in equation (1) to obtain the centripetal acceleration [tex]{a_c}[/tex] .
[tex]\begin{aligned}a_{c}&=\frac{(4\text{ m/s})^{2}}{37\text{ m}}\\&=\frac{16}{37}\text{ m/s}^{2}\\&=0.432\text{ m/s}^{2}\end{aligned}[/tex]
Therefore, the centripetal acceleration [tex]{a_c}[/tex] is [tex]0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}[/tex] .
Thus, the centripetal acceleration of runner at each end of track is [tex]\boxed{0.432{\text{ }}{{\text{m}}\mathord{\left/{\vphantom{{\text{m}}{{{\text{s}}^{\text{2}}}}}}\right.\kern-\nulldelimiterspace}{{{\text{s}}^{\text{2}}}}}}[/tex] .
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Circular Motion
Keywords:
Track, running, diameter, circle, runner, distance, moves, constant, speed, centripetal, acceleration, force, motion, uniform, radius, velocity and oval.
What are the solutions of the equation x4 – 5x2 – 14 = 0? Use factoring to solve.
Answer: The required solutions of the given equation are
[tex]x=\pm\sqrt7,~\pm\sqrt2i.[/tex]
Step-by-step explanation: We are given to find the solutions of the following bi-quadratic equation :
[tex]x^4-5x^2-14=0~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
Let us consider that
[tex]x^2=y~~~~~\Rightarrow x^4=y^2.[/tex]
So, equation (i) becomes
[tex]y^2-5y-14=0,[/tex]
which is a quadratic equation in the variable y. The above equation in variable y can be solved using factorization as follows :
[tex]y^2-5y-14=0\\\\\Rightarrow y^2-7y+2y-14=0\\\\\Rightarrow y(y-7)+2(y-7)=0\\\\\Rightarrow (y-7)(y+2)=0\\\\\Rightarrow y-7=0,~~~y+2=0\\\\\Rightarrow y=7,-2.[/tex]
Therefore, we get
[tex]x^2=7\\\\\Rightarrow x=\pm\sqrt7[/tex]
and
[tex]x^2=-2\\\\\Rightarrow x=\pm\sqrt{-2}\\\\\Rightarrow x=\pm\sqrt2i,~~~~~~~~~~~~~[\textup{where }i=\sqrt{-1}][/tex]
Thus, the required solutions of the given equation are
[tex]x=\pm\sqrt7,~\pm\sqrt2i.[/tex]
In the xy-plane, if line k has negative slope and passes through the point (−5,r), is the x-intercept of line k positive?
A fair coin is tossed 4 times. find the probability of obtaining exactly 2 heads
Final answer:
The probability of obtaining exactly 2 heads when a fair coin is tossed 4 times is 3/8.
Explanation:
To find the probability of obtaining exactly 2 heads when a fair coin is tossed 4 times, we need to determine the number of ways to get 2 heads out of 4 tosses and divide it by the total number of possible outcomes.
Step 1: Determine the number of ways to get exactly 2 heads.
There are four coin tosses, and we want 2 of them to be heads. We can choose the positions for the 2 heads out of the 4 tosses in 4C2 = 6 ways.
Step 2: Determine the total number of possible outcomes.
Each coin toss has two possible outcomes: heads or tails. Since there are 4 tosses, the total number of outcomes is 24 = 16.
Step 3: Calculate the probability.
The probability of obtaining exactly 2 heads is 6/16 = 3/8.
Baby Isbel plays with blocks. Each block is 3.7 inches tall. She has a collection of 41 blocks. If she could stack all the blocks on top of each other, how many inches tall would her tower of blocks be?
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Which fraction is between – 3/8 and – 9/16 on a number line?
the options are:
-15/ 32
-23/64
-5/16
-5/8
Simplify 4a + 8b - 6b + 2a
Answer:
The answer is 6a+2b
Step-by-step explanation:
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Charlene puts together two isosceles triangles so that they share a base, creating a kite. The legs of the triangles are 10 inches and 17 inches, respectively. If the length of the base for both triangles is 16 inches long, what is the length of the kite’s other diagonal?
Answer:
21 inches is right i just took the e2020 assignment
Step-by-step explanation:
a figure consisting of two points and all the points in between is a
Joanne deposits $4,300 into a one-year CD at a rate of 4.3%, compounded daily. How much interest does she earn?
In this case, Joanne's interest earned by depositing $4,300 into a one-year CD at a rate of 4.3%, compounded daily can be calculated by plugging the values into the formula.
To calculate the interest earned, use the formula for compound interest: I = P(1 + r/n)^nt - P, where I is the interest earned, P is the principal amount, r is the interest rate, n is the number of times the interest is compounded per time period, and t is the number of time periods.
Substitute the values into the formula to find the interest earned: I = $4,300(1 + 0.043/365)^(365*1) - $4,300
The ratio of men to women working for a company is 5 to 8 . if there are 104 women working for the company, what is the total number of employees?
How to do this I don’t understand what I’m doing wrong
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A number x is no more than 9 units away from 8. Write and solve an absolute-value inequality to show the range of possible values of x.
1. |x + 9| ≤ 8
−17 ≤ x ≤ −1
2. |x + 8| ≤ 9
−17 ≤ x ≤ 1
3. |x − 9| ≤ 8
1 ≤ x ≤ 17
4. |x − 8| ≤ 9
−1 ≤ x ≤ 17
Find the measure of Angle 1
Answer:
66º
Step-by-step explanation:
From the picture we know that AB║CD. Therefore, the line BD is a transversal line between two parallels.
We know that in these cases, the alternate interior angles are the same.
In the picture, angle 1 and the angle that measures 66º are alternate interior angles. Therefore, angle 1 measures 66º as well.
∠1 = 66º
What is the expression for "the difference between five times a number and twice that number"? 5(2 - n) 5n - 2n 2n - 5n?
A box of books has a mass of 4.10 kilograms for every meter of its Height . Convert this ratio into pounds per foot.
Answer:
0.498 on edg
Step-by-step explanation:
What is another way to express 64? A) 3 ^4 B) 6 ^4 C) 6.4 x 10^2 D) 8^2
What is the answer? Need help right away!!!!
Which statement best explains whether △JKL is congruent to △MNP?
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a rotation of 180° about the origin followed by a translation 2 units up.
△JKL is not congruent to △MNP because there is no sequence of rigid motions that maps △JKL to △MNP.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis.
△JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the x-axis followed by a rotation of 180° about the origin.
Two triangles are graphed on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. In triangle J K L, the vertex labeled as J lies on begin ordered pair negative 4 comma 2 end ordered pair. The vertex labeled as K lies on begin ordered pair negative 2 comma 3 end ordered pair. The vertex labeled as L lies on begin ordered pair negative 2 comma negative 1 end ordered pair. In triangle M N P, the vertex labeled as M lies on begin ordered pair 4 comma 0 end ordered pair. The vertex labeled as N lies on begin ordered pair 2 comma negative 1 end ordered pair. The vertex labeled as P lies on begin ordered pair 2 comma 3 end ordered pair.
△JKL is congruent to △MNP because it can be mapped to △MNP through a reflection across the y-axis and a translation 2 units up.
Explanation:To determine if △JKL is congruent to △MNP, we need to see if a series of rigid motions (rotations, reflections, translations) can map △JKL exactly onto △MNP. Looking at the positions of the vertices for both triangles, we can observe that if we carry out a reflection of △JKL across the y-axis (changing the sign of the x-coordinates) and then translate the reflected △JKL 2 units upward (+2 to the y-coordinates), we end up getting the vertices for △MNP. Therefore, △JKL is congruent to △MNP because △JKL can be mapped to △MNP by a reflection across the y-axis and a translation 2 units up. This option is not given explicitly in the original options, but this explanation provides the correct transformational sequence.
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The original price of the DVD is nine dollars the sale price is 80% of the price what is the sale price of the DVD?
multiply $9 by 80%
80% = 0.80
9 * 0.8 = 7.20
subtract that from original price
9 - 7.20 = 1.80
Sale price is $1.80
What is the percent increase of 2826 to 3324?
The answer is provided in the image attached.
Have a great day!
Which statement best describes the effect of replacing the function f(x) = 2x + 2 with the function g(x) = 2x - 3?
The graph shifts 1 unit left.
The graph shifts 5 units left.
The graph shifts 5 units right.
The graph shifts 1 unit right.
Amy deposited dimes and quarters into the coinstar machine at her local grocery store. The total money she deposited was $11.35.
What are the center and radius of the circle with equation (x + 8)^2 + (y + 3)^2 = 121?
Matter must have two physical properties: 1. have mass, and 2._____.
PLEASE HELP ME!!!! WORTH 10 POINTS!!
Write the point-slope form of the given line that passes through the points (-4, -1) and (3, -3). Identify (x1, y1) as (-4, -1).Include your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
Answer:
[tex]y-(-1)=-\frac{2}{7}(x-(-4))[/tex]
Step-by-step explanation:
We know that the line passes through (-4,-1) and (3,-3), where [tex](x_{1} ,y_{1} )[/tex] is [tex](-4,-1)[/tex] and [tex](x_{2} ,y_{2} )[/tex] is [tex](3,-3)[/tex].
First, we need to find the slope with the formula
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Replacing given points
[tex]m=\frac{-3-(-1)}{3-(-4)}=\frac{-3+1}{3+4}=\frac{-2}{7}[/tex]
Then, we use the slope, one point and the slope-point form
[tex]y-y_{1} =m(x-x_{1} )\\y-(-1)=-\frac{2}{7}(x-(-4))\\ y+1=-\frac{2}{7}x+\frac{8}{7} \\y=-\frac{2}{7}x+\frac{8}{7}-1\\y=-\frac{2}{7}x+\frac{8-7}{7} \\y=-\frac{2}{7}x+\frac{1}{7}[/tex]
The slope-intercept form is
[tex]y=-\frac{2}{7}x+\frac{1}{7}[/tex]
The point-slope form is
[tex]y-(-1)=-\frac{2}{7}(x-(-4))[/tex]
Given: p: 2x = 16 q: 3x – 4 = 20 Which is the converse of p → q?
Answer:
If q:3x-4=20 then p:2x=16
Step-by-step explanation:
We are given that two statement p and q
p:2x=16
q:3x-4=20
We have to find the converse of given statements.
Converse:
If p then q.
Converse statement
If q then p.
[tex]q\implies p[/tex]
Therefore, definition of converse
q: 3x-4=20
p: 2x=16
If q:3x-4=20 then p:2x=16
2. How are Angle 3 and Angle 7 related?
1 point
Corresponding angles
Vertical angles
Same Side Interior angles
Alternate exterior angles
Rolando had $200,000 in a CD at Big Bucks Bank, which just failed. If the FDIC insurance the bank, how much will Rolando get back?
$0
$250,000
$120,000
$200,000
HELP ME PLZ PPL!!!!
Solve for x: |x − 2| + 10 = 12 (1 point)
x = −20 and x = 4
x = −4 and x = 0
No solution
x = 0 and x = 4