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
Sedaia [141]
3 years ago
11

A runner sprints around a circular track of radius 130 m at a constant speed of 7 m/s. The runner's friend is standing at a dist

ance 260 m from the center of the track. How fast is the distance between the friends changing when the distance between them is 260 m? (Round your answer to two decimal places.)\
Physics
1 answer:
mylen [45]3 years ago
8 0

Answer: 6.78 m/sec

Explanation:

Let the track be centered at origin, with radius = 130

Let θ = angle formed by line from centre to runner with positive x-axis

Let S = distance along circular track where runner is located

and where S = 0 is at position (130,0)

Runner sprints at constant speed of 7m/sec . . . . ds/dt = 7

Formula for arc length:

s = r θ

s = 130 θ

d/dt = 130 dθ/dt

7 = 130 dθ/dt

dθ/dt = 7/130

Now,

Let (x,y) be runners position

x = r cos(θ) = 130 cos(θ)

y = r sin(θ) = 130 sin(θ)

x² + y² = r² = 16,900

Let runner's friend be at position (260, 0) (angle of 0 degrees with positive x-axis)

Let D = distance from runner to runner's friend

D² = (260 - x)² + y²

D² = 67,600 - 520x + x² + y²

D² = 67,600 - 520x + 16,900

D² = 84,500 - 520(130 cos(θ))

D² = 84,500 - 67,600 cos(θ)

Differentiating both sides with respect to t, we get

2D dD/dt = 67,600 sin(θ) dθ/dt

Find dD/dt when D = 260

First, we find θ when D = 260 using formula

D² = 84,500 - 67,600 cos(θ)

67,600 = 84,500 - 67,600 cos(θ)

67,600 cos(θ) = 16,900

cos(θ) = 1/4

sin(θ) = √(1 - (1/4)²) = √(15/16) = √15/4

Now we can calculate dD/dt

2D dD/dt = 67,600 sin(θ) dθ/dt

2(260) dD/dt = 67,600 * √15/4 * 7/130

dD/dt = 67,600/520 * √15/4 * 7/130

dD/dt = 7√15/4

dD/dt = 6.77772

Distance between the friends is changing at a rate of 6.78 m/sec

You might be interested in
A 45-mH inductor is connected in series with a 60-Ω resistor through a 15-V dc power supply and a switch. If the switch is close
egoroff_w [7]

Answer:

The current is 0.248 A

Explanation:

Given that,

Inductor L= 45\times10^{3}\ H

Resistance R= 60\Omega

Voltage = 15 volt

Time t =7.0\times10^{-3}\ sec

We need to calculate the current

Using formula of current

I=\dfrac{V}{R}(1-e^{\dfrac{-R}{L}}t)

Where, V = voltage

R = resistance

L = inductance

T = time

Put the value into the formula

I=\dfrac{15}{60}(1-e^{\dfrac{-60}{45\times10^{3}}}\times7\times10^{-3})

I=0.248\ A

Hence, The current is 0.248 A.

4 0
3 years ago
A mechanic turns a wrench using a force of 27.00 N at a distance of 16.00 cm from the rotation axis. The force is perpendicular
lutik1710 [3]

Answer:4.32Nm

Explanation:

The magnitude of the torque will be the product of the force and its perpendicular distance from the force.

Force = 27N

Perpendicular distance = 16cm = 0.16m

Torque = 27×0.16

Torque = 4.32Nm

3 0
3 years ago
What type of force pulls in two opposite directions?
torisob [31]
Tensional forces which is associated with normal faults
7 0
3 years ago
Read 2 more answers
Use the drop-down menus to identify the variables for the second hypothesis.
Debora [2.8K]

Answer: 1) independent

2) dependent

3) voltage

Explanation:

8 0
3 years ago
Read 2 more answers
Two representative elements are in the same period of the periodic table. Which statement correctly describes the atoms of the t
sveticcg [70]

1) They have valence electrons in the same energy level.

2) Helium atoms have 2 valence electrons, while atoms of the other elements in the group all have 8 valence electrons.

3) cesium (Cs)

4) There are two electrons in the first energy level and seven electrons in the second energy level.

In the periodic table, elements are arranged in order of increasing atomic number into groups and periods.

In the periodic table, we have an arrangement of atoms based on their respective groups and periods.

If I pick two representative elements in the same period, their number of valence electrons will differ by 1 but they will all be accommodated in the same energy level.

Helium is the first member of group 18. Unlike the other members of the group, its first shell is also its valence shell. It has two and not eight valence electrons like other members of the group.

The electronic configuration of Ca is [Ar] 4s², that of Li is [He] 2s1, that of Cs is [Xe] 6s1, that of Br is [Ar] 4s² 3d¹⁰ 4p⁵ and that of oxygen is [He] 2s² 2p⁴.

We can see that only Cs has  valence electrons in higher energy orbitals than those of Ca.

Lastly, Fluorine is in group 17. There are nine electrons in this atoms. They arranged in such a way that there are two electrons in the first shell and seven electrons in the second shell.

Learn more:brainly.com/question/24384700

7 0
3 years ago
Other questions:
  • Two vectors A and B are added together to form a vector C. The relationship between the magnitudes of the vectors is given by A
    6·1 answer
  • _____ is the horizontal change between two points on the line.
    7·2 answers
  • What is the stopping distance at night for a passenger vehicle traveling at 50 mph?
    12·1 answer
  • Helppp plss
    13·1 answer
  • I will fan and give 2 medals!!!!!!
    8·1 answer
  • If an object doubles in mass, what happens to its inertia?
    14·1 answer
  • 1. What is the relationship between wavelength and the penetrating power of an electromagnetic wave?
    13·1 answer
  • Which statement correctly describes the differences between positive and negative acceleration?
    12·1 answer
  • A lorry pulls forward after initially being stationary, it takes the lorry 80m to reach a speed of
    12·1 answer
  • 3. Which resistor experiences a larger voltage drop across it?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!