A softball player is testing her physics knowledge and tosses a softball upward from the top of a building. The building is 100 m tall and the ball starts with a velocity of 10 m/s.a. What is the maximum height the ball reaches and at what time? b. How much time does it take for the ball to go from h=50 m to h=0 m on the way down? c. What is the velocity when h=50 m?

Answers

Answer 1

Answer:

Explanation:

We shall apply newton's laws formula

a )

initial velocity in upward direction u = 10 m/s

acceleration due to gravity g = 9.8/ m .s²

Let h be the maximum height where v = o

v² = u² - 2gh

0 = 10² - 2 gh

h = 10² / 2g

= 10² /  2  x 9.8

= 5.10 m

Since the ball was thrown from height of 100 m , total maximum height of ball

= 100 + 5.10

= 105.10 m

Let t be the time taken

v = u - gt

0 = 10 - gt

t = 10 / 9.8

= 1.02 s

b )

when h = 50 on its way downwards , velocity

v² = u² + 2 g s  

v² = 0 + 2 x 9.8 x ( 105.10 - 50 )

[  distance travelled by ball at this point from top = 105.1 - 50 = 55.10 ]

v = 32.86 m / s

Let us find out final velocity of touching the ground . For it distance travelled = 105.10

v² = u² + 2gh

v² = 0 + 2 x 9.8 x 105.1

v = 45.39 m /s

Now velocity at h = 50 is 32.86

velocity at h = 0 is 45.39

time taken to travel fro h = 50 to h = 0

v = u + gt

45 .39 = 32.86 + 9.8 x t

t =  1.28 s .


Related Questions

What is correct regarding an ideal isotropic antenna? a. An ideal isotropic antenna is a highly efficient antenna used extensively in today’s communication systems b. An ideal isotropic antenna is a specialized antenna used to direct EM signal energy towards a specific direction c. An ideal isotropic antenna is a theoretical antenna that does not exist in practice, but is useful in explaining power density and unguided EM signal attenuation d. None of the above are correct statements

Answers

Answer:

C An ideal isotropic antenna is a theoretical antenna that does not exist in practice, but is useful in explaining power density and unguided EM signal attenuation

Explanation:

Because practically speaking there is no ideal isotropic antenna it is only imaginary radiating in all directions and use as an arbitrary point for antenna gain

Which lists the elements in order from most conductive to least conductive?

potassium (K), selenium (Se), germanium (Ge)
germanium (Ge), potassium (K), selenium (Se)
selenium (Se), germanium (Ge), potassium (K)
potassium (K), germanium (Ge), selenium (Se)

Answers

Answer:

Answer: potassium (K) germanium (Ge) selenium (Se)

Explanation:

I just took the test, the farther to the right on the periodic table you go the less conductive it gets.

Answer:

Answer: potassium (K) germanium (Ge) selenium (Se)

Explanation:

The most conductive to least conductive is from left to right

The acceleration of a piston is given by : rw^2 cos(wt-pi/4) find amplitude.

Answers

Given :

The acceleration of a piston is given by :

[tex]a=r\omega^2cos\ (\omega t-\dfrac{\pi}{4})[/tex]

To Find :

The amplitude of the acceleration of piston .

Solution :

Now , acceleration is :

[tex]a=r\omega^2cos\ (\omega t-\dfrac{\pi}{4})[/tex]

Now , amplitude is maximum of any function .

So , maximum value of [tex]cos\ \theta[/tex] is equal to 1 .

Therefore , amplitude of the acceleration of piston is :

[tex]A=r\omega^2[/tex]

Hence , this is the required solution .

The deck of a bridge is suspended 235 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 235 − 16t^2.

Required:
a. Find the average velocity (in ft/s) of the pebble for the time period beginning when t = 2 and lasting the following amount of time.

1. 0.1 sec:________
2. 0.05 sec:_______
3. 0.01 sec:_______

b. Estimate the instantaneous velocity (in ft/s) of the pebble after 3 seconds. ft/s.

Answers

Answer:

(a) 1, average velocity = -65.6 m/s

   2, average velocity = -64.8 m/s

   3, average velocity = -64.16 m/s

(b) The instantaneous velocity is -96 m/s

Explanation:

(a)

Average velocity is given  by;

[tex]y(t_2,t_1) = \frac{y(t_2) - y(t_1)}{t_2-t_1}[/tex]

(1)

[tex]y(2.1,2) = \frac{(235-16*2.1^2) - (235-16*2^2)}{2.1-2}\\\\ y(2.1,2) = -65.6 \ m/s[/tex]

(2)

[tex]y(2.05,2) = \frac{(235-16*2.05^2) - (235-16*2^2)}{2.05-2}\\\\ y(2.05,2) = -64.8 \ m/s[/tex]

(3)

[tex]y(2.01,2) = \frac{(235-16*2.01^2) - (235-16*2^2)}{2.01-2}\\\\ y(2.01,2) = -64.16 \ m/s[/tex]

b. y = 235 - 16t²

The instantaneous velocity is given by;

v = dy /dt

dy / dt = -32t

when t = 3 s

v = -32(3)

v = -96 m/s

(a)The average velocity for the 0.1 sec,0.05 sec,0.01 sec will be  -65.6 m/s, -64.8 m/s and -64.16 m/s respectively.

What is the average velocity?

The total displacement traveled by an object divided by the total time taken is the average velocity.

Average velocity is given by;

[tex]\rm y(t_2,t_1)=\frac{y(t_2)-y(t_1)}{t_2-t_1} \\\\[/tex]

The average velocity for case 1;

[tex]\rm y(2.1,2)=\frac{(235-16\times 2\times 1^2)-(235-16 \times 2^2)}{2.1-2} \\\\ \rm y(2.1,2)=\-65.6 \ m/sec[/tex]

The average velocity for case 2;

[tex]\rm y(2.015,2)=\frac{(235-16\times 2.05^2)-(235-16 \times 2^2)}{2.05-2} \\\\ \rm y(2.1,2)=\-64.8 \ m/sec[/tex]

The average velocity for case 3;

[tex]\rm y(2.01,2)=\frac{(235-16\times 2.01^2)-(235-16 \times 2^2)}{2.01-2} \\\\ \rm y(2.1,2)=\-64.16 \ m/sec[/tex]

Hence the average velocity for the 0.1 sec,0.05 sec,0.01 sec will be  -65.6 m/s, -64.8 m/s and -64.16 m/s respectively.

(b) The instantaneous velocity will be -96 m/s.

The given equation in the problem is;

[tex]\rm y = 235 - 16t^2[/tex]

The instantaneous velocity is given as;

[tex]v = \frac{dy}{dt} \\\\ \frac{dy}{dt} = -32t\\\\ t = 3 s\\\\ v = -32\times 3\\\\ v = -96 m/s[/tex]

Hence the instantaneous velocity will be -96 m/s.

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An object is moving in a negative direction with a negative acceleration, for example an object dropped out a window. What does it mean that both velocity and acceleration are negative?

Answers

Answer:

yes bc they are falling :]

Explanation:

a car moves 8 m in 4 s at a comstant velocity. what is the cars acceleration

Answers

Answer:

Zero.

Explanation:

Acceleration is defined as change in velocity per unit time. For constant, the acceleration is zero.

      [tex]\hat{a} =\frac{ \delta V}{t}[/tex]

as [tex]\delta[/tex][tex]v\\[/tex] is zero.

Give three examples of unbalanced forces in your everyday life. HELP FAST PLZ

Answers

1. Kicking a soccer ball
2.Playing tug of war
3.Bouncing a Ball

Answer:

1.    Kicking a soccer ball

2.      Playing tug of war  

3.         Bouncing a Ball

Explanation:

An isolated system contains two objects with charges q1q1 and q2q2. If the charge on object 1 is doubled, what is the charge on object 2? g

Answers

Answer:

The new charge on the second object is q₂ - q₁

Explanation:

Given;

charge on the first object,  q₁

charge on the second object, q₂

Since there is no external force on isolated system, the total charge in the system is given by;

Q = q₁ + q₂

q₂ = Q - q₁

When the charge on object 1 is doubled, q₁' = 2q₁

let q₂' be the new charge on object 2

q₂' = Q - q₁'

q₂' = (q₁ + q₂) - 2q₁

q₂' = q₁ + q₂ - 2q₁

q₂' = q₂ - q₁

Therefore, the new charge on the second object is q₂ - q₁

The charge on object 2 will be "q₂ - q₁".

Charge on object:

The charge's quantity on such an item represents the degree of imbalance between its electrons as well as protons.

Just to calculate the overall charge of a positively (+) charged item, divide the total no. of valence electrons by the overall number of protons.

According to the question,

Object 1's charge = q₁

Object 2's charge = q₂

Let,

New charge of object 2 be "q₂'".

 

The total charge in the system will be:

Q = q₁ + q₂

or,

q₂ = Q - q₁

hence,

The charge on object 2 be:

q₂' = Q - q₁'

By substituting the values,

        = (q₁ + q₂) - 2q₁

        = q₁ + q₂ - 2q₁

        = q₂ - q₁                

Thus the answer above is appropriate.

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Why si unit develop all over the world?​

Answers

Answer:

SI unit is used in most places around the world, so our use of it allows scientists from disparate regions to use a single standard in communicating scientific data without vocabulary confusion.

Explanation:

hope it helps

Si unit is used almost all around the world, so our use of it allows

Scientist from disparate regions to use a single standered in communicating scientific data without vocabulary confusion

what is the difference between each distance traveled and displacement travled

Answers

Displacement is a vector magnitude that depends on the position of the body which is individualistic for the trajectory.

While, Distance is a scalar magnitude that measures over the trajectory.

.A cart rolling down an incline for 5.0 seconds has an acceleration of 1.6 m/s2. If the cart has a beginning speed of 2.0 m/s, and its final velocity of 10 m/s, what was the car's displacement?

Answers

Use the formula,

[tex]\Delta x=v_it+\dfrac12at^2[/tex]

where [tex]\Delta x[/tex] is the cart's displacement (from the origin), [tex]v_i[/tex] is its initial speed, [tex]a[/tex] is its acceleration, and [tex]t[/tex] is time.

[tex]\Delta x=\left(2.0\dfrac{\rm m}{\rm s}\right)(5.0\,\mathrm s)+\dfrac12\left(1.6\dfrac{\rm m}{\mathrm s^2}\right)(5.0\,\mathrm s)^2[/tex]

[tex]\implies\boxed{\Delta x=30\,\mathrm m}[/tex]

Alternatively, since acceleration is constant, we have

[tex]\dfrac{v_f+v_i}2=\dfrac{\Delta x}t[/tex]

That is, we have these two equivalent expressions for average velocity, where [tex]v_f[/tex] is the cart's final velocity. Solve for [tex]\Delta x[/tex]:

[tex]\dfrac{10\frac{\rm m}{\rm s}+2.0\frac{\rm m}{\rm s}}2=\dfrac{\Delta x}{5.0\,\mathrm s}[/tex]

[tex]\implies\boxed{\Delta x=30\,\mathrm m}[/tex]

If a cheetah could maintain its top speed of 120 km/h for 20 minutes, how far would it run?

Answers

Alright. If it’s running at a constant speed of 120 km/h, in one hour it will have traveled 120 kilometers. hence “kilometers per hour”

20 minutes is 1/3 of an hour so 120/3 will be 40

therefore, in 20 minutes the cheetah would’ve ran 40km if it maintained 120km/h for 20 minutes.

How do you play Simon says?

Answers

This is how you play
One person is Simon
If the person who is Simon say “Simon say (direction)” you do it but if he doesn’t say Simon says don’t do it or your out

26.0 g of copper pellets are removed from a 300∘C oven and immediately dropped into 120 mL of water at 21.0 ∘C in an insulated cup.What will the new water temperature be?

Answers

Answer:

The new water temperature is 26.4 °C

Explanation:

Given;

mass of copper, [tex]M_{cu}[/tex] = 26 g = 0.026 kg

temperature of copper, t = 300 °C

volume of water, V = 120 mL = 0.12 L

temperature of water, t = 21 °C

density of water, ρ = 1 kg/L

mass of water = density x volume

mass of water = (1 kg/L) x 0.12 L = 0.12 kg

heat lost by copper = heat gained by water

Both copper and water reach final temperature, T

Heat gained by water, [tex]Q_w[/tex] = [tex]m_w[/tex]cΔθ = [tex]m_w C(T - t)[/tex]

[tex]Q_w = m_w C(T - t)\\\\Q_w = 0.12*4200(T-21)\\\\Q_w = 504(T-21)[/tex]

Heat lost by copper is given by;

[tex]Q_{cu} = m_{cu}C(300-T)\\\\Q_{cu} = 0.026*385(300-T)\\\\Q_{cu} = 10.01(300 - T)[/tex]

[tex]Q_{cu} = Q_w[/tex]

504(T- 21) = 10.01(300 - T)

504 T - 10584 = 3003 - 10.01 T

504 T + 10.01 T= 3003 + 10584

514.01 T = 13587

T = (13587) / 514.01

T = 26.4 °C

Therefore, the new water temperature is 26.4 °C

The new water temperature using the given parameters is;

26.49°C

We are given;

Mass of copper; m_cu = 26 g = 0.026 kg

Temperature; T_cu = 300 °C

Volume of water; V = 120 mL = 0.12 L

Temperature of water, T_w = 21 °C

Density of water; ρ = 1 kg/L

Let us find the mass of water from the formula;

m_w = ρ × V

m_w = 1 × 0.12

m_w = 0.12 kg

Now, from the principle of conservation of energy, we can say that the total heat lost by a hot body is equal to the total heat gained by a cold body.

The hot body here is copper while the cold body is water. Thus;

Heat lost by copper = Heat gained by water

Formula for heat lost by copper is;

Q_cu = m_cu * c_cu * (T_f - T_cu)

Formula for heat gained by water is;

Q_w = m_w * c_w * (T_f - T_w)

Where;

T_f is final temperature reached by copper and water

c_cu is specific heat capacity of copper = 385 J/kg.°C

c_w is specific heat capacity of water = 4200 J/kg.°C

Thus;

Q_cu = 0.026 × 385 × (300 - T_f)

Q_cu = 3030 - 10.01T_f

similarly;

Q_w = 0.12 × 4200 × (T_f - 21)

Q_w = 504T_f - 10584

Thus;

3030 - 10.01T_f = 504T_f - 10584

3030 + 10584 = 504T_f + 10.01T_f

13614 = 514.01T_f

T_f = 13614/514.01

T_f = 26.49°C

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[tex]\huge{\gray{\sf Question:} }[/tex]

A body describes simple harmonic motion with an amplitude of 5 cm and a period of 0.2 s. Find the acceleration and velocity of the body when the displacement is (a) 5 cm, (b) 3 cm and (c) 0 cm.​

Answers

Answer:

ANSWER

A = 5 cm = 0.05 m

T = 0.2 s

ω=2π/T=2π/0.2=10πrad/s

plz give brainlist

hope this helped

Answer:

[tex]here \: amplitude = 5cm (convert \: to \: si \: unit) = .05m \\ t = .2sec \\ omega = \frac{2\pi}{t} \\ = \frac{2\pi}{.2 } = 10\pi \frac{rad}{s} \\ we \: want \: find \: a \: and \: v \\ we \: know \: that \: a = - {omega}^{2} x \\ v = omega \sqrt{ {r}^{2} - {x}^{2} } \\(1)x = .05m \\ a = - {10\pi}^{2} \times .05 = - 5 {\pi}^{2} \frac{m}{ {s}^{2} } \\ v = 10\pi \sqrt{ {.05}^{2} - {.05}^{2} } = 0 \\ 2)x = 3cm = .03m \\ a = {(10\pi)}^{2} \times .03 = - 3 {\pi}^{2} \frac{m}{ {s}^{2} } \\ v = 10\pi \sqrt{ {.05}^{2} - {.03}^{2} } = 10\pi \times .04 = .4\pi \frac{m}{s} \\ 3)x = 0 \\ a = - {(10\pi)}^{2} \times 0 = 0 \\ v = 10\pi \times \sqrt{ {.05}^{2} - {0}^{2} } = - 10\pi \times .05 = .5\pi \frac{m}{s} \\ thank \: you[/tex]

Place gamma rays, infrared, microwaves, radio waves, ultraviolet, visible light, and x-rays in order from largest wavelength to smallest wavelength.

Answers

Answer:

Going by EM SPECTRUM WE HAVE

radio waves, microwaves, infrared, VISIBLE LIGHT, ultraviolet, X-rays, GAMMA RAYS

Explanation:

BECAUSE

V= WAVELENGTH/ FREQUENCY

AS FREQUENCY INCREASES WAVELENGTH DECREASE AN VICE VERSA

How do scientists use the evidence they gather?

Answers

Answer:

When conducting research, scientists use the scientific method to collect measurable, empirical evidence in an experiment related to a hypothesis (often in the form of an if/then statement), the results aiming to support or contradict a theory.

Convert the following to SI units:_______. a. 9.12μs9.12μs b. 3.42 km c. 44 cm/ms d. 80 km/h

Answers

Answer:

Explanation:

A. We know that 1microsecond= 10^-6s

So = 9.12*10^-6=9.12*10^-6s

B 1km= 1000m

So 3.42km= 3240m

C.1ms= 10^-3s

And 1cm= 10^-2m

So 44*10^-2m/10^-3s=440m/s

D. 80km/hr= 80*1000/3600= 22.2m/s

Because 1km= 1000m

1hr= 3600s

Part A. 13 in Express your answer to two significant figures and include the appropriate units. SubmitPrev Previous Answers Request Answer X Incorrect; Try Again; 5 attempts remaining Part B. 77 ft/s Express your answer to two significant figures and include the appropriate units ,, ? Value m/s

Answers

Answer:

Part A

[tex]x = 0.33 \ m[/tex]

Part B

[tex]y = 23.49 \ m/s[/tex]

Explanation:

From the question we are told to convert

    13 inches to meters

Now

     1 in   =   0.0254 \  m

      13 \  in  =  x  m

=>  [tex]x = \frac{13 * 0.0254 }{1}[/tex]

=>     [tex]x = 0.33 \ m[/tex]

For  part B  we are told to covert 77ft/s  to meters /srconds

   So  

         1 ft/s  =  0.305 \ m/s  

         77 ft/s  =  y

=>      [tex]y = \frac{77 * 0.305 }{1}[/tex]

=>     [tex]y = 23.49 \ m/s[/tex]

Light travels at 3 × 108 m/s, and it takes about 8 min for light from the sun to travel to Earth. Based on this, the order of magnitude of the distance from the sun to Earth is g

Answers

Answer:

The order of magnitude of the distance from the sun to Earth is 10⁸ km.

Explanation:

The order of magnitude of the distance from the sun to Earth can be calculated as follows:

[tex] c = \frac{x}{t} [/tex]

Where:

c: is the speed of light = 3x10⁸ m/s

t: is the time = 8 min

Hence, the distance is:

[tex] x = c*t = 3 \cdot 10^{8} m/s*8 min*\frac{60 s}{1 min} = 1.44 \cdot 10^{11} m = 1.44 \cdot 10^{8} km [/tex]

Therefore, the order of magnitude of the distance from the sun to Earth is 10⁸ km.

I hope it helps you!

Given that the lines are parallel, what would be the value of angle "a" in the diagram found below?

Answers

Explanation:

Hey there!!

a = 40° { corresponding angles on a parallel lines are equal}.

As A and B are parallel, a and 40° are corresponding angles.

Hope it helps...

The value of angle "a" will be 40°

What is corresponding angle ?

The angles which are on the same side of one of two lines cut by a transversal and are on the same side of the transversal is called corresponding angles.

since , angle a and angle B = 40° (given) are on the same relative position at the intersection where a straight line crosses two others and since both the lines are parallel to each other hence ,both the angles are said to be corresponding angles .This implies both the angles must be equal .

angle a = 40°

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Can air make shadows

Answers

Answer:no

Explanation:the way to see air is by steaming something sometimes you might not see the air but you can see the shadow

μN/(kg⋅ns) in the correct SI of:________

Answers

Answer:

μN/ (kg ns) = 10³ N / (kg s)

Explanation:

In this exercise they ask us if the notation is correct. Let's write the different terms in the SI systems

force is N

time is in seconds

the unit given for the force is 1 N = 10⁶ μN

the unit of time is 1 s = 10⁹ ns

the correct way to give the answer should be: N / (kg s)

so the notation should be changed

        μN /kg ns = μN / (kg ns) (1N / 10⁶ μN) (10⁹ ns / 1 s) =

        μN/ (kg ns) = 10³ N / (kg s)

Circle all true statements:
a) Water at 90°C is warmer than water at 202°F
b) 40K corresponds to -40°C
c) Temperature differing by 25 on the Fahrenheit scale must differ by 45 on the Celsius scale.
d) Temperatures which differ by 10 on the Celsius scale must differ by 18 on the Fahrenheit scale.
e) 0°F corresponds to -32°C.

Answers

Answer:

The true statements are:

c) Temperature differing by 25 on the Fahrenheit scale must differ by 45 on the Celsius scale.

d) Temperatures which differ by 10 on the Celsius scale must differ by 18 on the Fahrenheit scale.

Explanation:

option a is false, 90°C is equal to 194°F which is not warmer than 202°F

option b is false, 40K is equal to -233°C

option e is false 0°F corresponds to -17.8°C.

A ball easily moves but not a bus when we push them. why?

Answers

Answer: The amount of matter is higher in a bus than a ball.

Explanation:

Scientists might use a diagram to model the water cycle. What are two
benefits of this model?

Answers

Answer:

B, and D

Explanation:

The two benefits of this model is it specify a process that is very complex. It can represent changes that occur very slowly. Thus option B and D is correct.

What is water cycle?

The water cycle is defined as a cycle of events that involves precipitation as rain and snow, drainage in streams and rivers, and return to the atmosphere by evaporation and transpiration. Water moves through this cycle between the earth's oceans, atmosphere, and land.

It can also be defined as the route all water takes as it travels around Earth in various conditions.

There are basically six stages of water cycle.

EvaporationSublimationCondensationPrecipitationInfiltrationRunoff

Thus, the two benefits of this model is it specify a process that is very complex. It can represent changes that occur very slowly. Thus option B and D is correct.

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Force is the amount _____ or _____ on an object



Motion is the action of _____ from one place to another place.

Answers

Answer:

force is the amount of work or pressure given to an object

motion is the action of moving one place to another place

The position of a particle is given by the function x = \left(2t^3 - 6t^2 + 12\right) m, where t is in s. Question:At what time is the acceleration zero? (with working out)

Answers

Answer:

t = 1sec

Explanation:

Given the position of a particle  expressed by the equation x = (2t^3 - 6t^2 + 12)m, where t is in seconds, the acceleration function can be gotten by taking the second derivative of the function with respect to t as shown;

a = d/dt(dx/dt)

First let us get dx/dt

dx/dt = 3(2)t³⁻¹-2(6)t²⁻¹+0

dx/dt = 6t²-12t

a = d/dt(dx/dt)

a = d/dx(6t²-12t)

a = 2(6)t²⁻¹-12t¹⁻¹

a = 12t - 12t⁰

a = 12t-12

If the acceleration is zero, then;

12t-12 = 0

add 12 to both sides

12t-12+12 = 0+12

12t = 12

t = 12/12

t = 1sec

Hence the time when acceleration is zero is 1sec

What is the latitude of the vertical (direct) rays of the sun?

Answers

Answer:

23.5 degree North

Explanation:

The latitude of the vertical (direct) rays of the sun is 23.5 degree North. This is however due to the sun's vertical rays being located directly above 23.5 degree South which is the position of the Tropic of Capricorn.

The sun ray is highest at this pap tion and it occurs during Summer solstice which happens between June 21 / 22 of every year.

Two positive charges q1 = q2 = 2.0 μC are located at x = 0, y = 0.30 m and x = 0, y = -0.30 m, respectively. Third point charge Q = 4.0 μC is located at x = 0.40 m, y = 0.What is the net force ((a)magnitude and (b)direction) on charge q1 exerted by the other two charges?

Answers

Answer:

 F = 0.111015 N

Explanation:

For this exercise the force is given by Coulomb's law

        F = k q₁q₂ / r₂₁²

we calculate the electric force of the other two particles on the charge q1

Charges q₁ and q₂

the distance between them is

          r₁₂ = y₁ -y₂

          r₁₂ = 0.30 + 0.30

          r₁₂ = 0.60 m

let's calculate

          F₁₂ = 9 10⁹ 2 10⁻⁶ 2 10⁻⁶ / 0.60 2

          F₁₂ = 1 10⁻¹ N

directed towards the positive side of the y-axis

Charges 1 and 3

Let's find the distance using the Pythagorean Theorem

             r₁₃ = RA [(0.40-0) 2 + (0-0.30) 2]

             r₁₃ = 0.50 m

            F₁₃ = 9 10⁹ 2 10⁻⁶ 4 10⁻⁶ / 0.50²

            F₁₃ = 1.697 10⁻² N

The direction of this force is on the line that joins the two charges (1 and 3), let's use trigonometry to find the components of this force

           tan θ = y / x

           θ = tan⁻¹ y / x

          θ = tan⁻¹ 0.3 / 0.4

           tea = 36.87º

    The angle from the positive side of the x-axis is

         θ ’= 180 - θ

        θ ’= 180 - 36.87

        θ ’= 143.13º

       sin143.13 = F_13y / F₁₃

           F_13y = F₁₃ sin 143.13

           F{13y} = 1.697 10⁻² sin 143.13

           F_13y = 1.0183 10⁻² N

            cos 143.13 = F_13x / F₁₃

           F₁₃ₓ = F₁₃ cos 143.13

           F₁₃ₓ = 1.697 10⁻² cos 143.13

           F₁₃ₓ = -1.357 10-2 N

Now we can find the components of the resultant force

          Fx = F13x + F12x

          Fx = -1,357 10-2 +0

          Fx = -1.357 10-2 N

          Fy = F13y + F12y

         Fy = 1.0183 10-2 + ​​1 10-1

          Fy = 0.110183 N

We use the Pythagorean theorem to find the modulus

         F = Ra (Fx2 + Fy2)

         F = RA [(1.357 10-2) 2 + 0.110183 2]

         F = 0.111015 N

Let's use trigonometry for the angles

         tan tea = Fy / Fx

          tea = tan-1 (0.110183 / -0.01357)

          tea = 1,448 rad

to find the angle about the positive side of the + x axis

           tea '= pi - 1,448

           Tea = 1.6936 rad

The magnitude of the net force on q1 exerted by the other two charges is 0.357 N.

The direction of the net force on q1 is 50⁰.

The given parameters;

q1 = 2.0 μC located at (0, 0.3) mq2 = 2.0 μC located at (0, -0.3) mq3 = 4.0 μC located at (0.4, 0) m

The force on q1 due to q2 occurs only in y-direction and can be calculated using Coulomb's law as shown below;

[tex]F_1_2 = \frac{kq^2}{r^2}j = \frac{(9\times 10^9) \times (2\times 10^{-6})^2 }{(0.3 +0.3)^2} j \\\\\F_{12} = (0.1)j[/tex]

The force on q1 due to q3 occurs both in x-direction and y-direction, and it is calculated as follows;

[tex]distance \ between \ q1 \ and \ q3\ , r_{13} = \sqrt{0.3^2 \ + \ 0.4^2} = 0.5 \ m\\\\F_{13} = \frac{kq^2}{r_{13}^2} (\frac{0.4i}{0.5} \ + \ \frac{0.3j}{0.5} )\\\\F_{13} = \frac{kq^2}{r_{13}^2} (0.8i + 0.6j)\\\\F_{13} = \frac{9\times 10^9 \times (2\times 10^{-6}) \times (4\times 10^{-6})}{0.5^2} (0.8i + 0.6j)\\\\F_{13} = 0.288(0.8i + 0.6j)\\\\F_{13} = 0.23i + 0.173j[/tex]

The net force is calculated as follows;

[tex]F_{net} = F_{12} \ + \ F_{13}\\\\F_{net} = (0.1j) \ + \ (0.23i + 0.173j)\\\\F_{net} = (0.23i + 0.273j)[/tex]

The magnitude of the net force on q1 is calculated as follows;

[tex]|F| = \sqrt{(0.23^2) \ + \ (0.273^2)} \\\\|F| = 0.357 \ N[/tex]

The direction of the net force on q1 is calculated as follows;

[tex]tan(\theta )= \frac{F_y}{F_x} \\\\\theta = tan^{-1} (\frac{0.273}{0.23} )\\\\\theta = 50^0[/tex]

Learn more here:https://brainly.com/question/17132341

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