Two positive point charges q are placed on the x-axis, one at x = a and one at x = -a.a. Derive an expression for the electric field at points on the x-axis, where ?a < x < a.

Answer: They change the shape of the lens

Explanation: It enables the lens to change its shape to focus on objects at various distances

A liquid vat with a 1.90 m diameter is 2.10 m deep. 1.30 atm of pressure is present at the vat's bottom. The amount of liquid in the container weighs 2788kg

Suppose we define d as the liquid's density;

The pressure at the bottom of the vat, which has a depth (h), can then be calculated as P = P0+Dgh, where P0 is atmospheric pressure.

P-P0 = Dgh

D= P-P0/gh

We are aware that density (D) = mass/volume m/v = P-P0/gh.

Volume equals area times height, hence the formula for mass is: m = P-P0/gh x area (a) x height (h) = (P-P0)/gh x π(d/2)^2

Given that P = 1.3 atm and P0 = 1 atm, the diameter of the vat (d) is 1.9 atm, which is

(1.3-1)/9.8 x (1.9/2)2 x 1.013 x 105 Pa, = 2788 kg.

As a result, we can say that the mass of the liquid in the vat is 2788kg

To learn more about pressure click here https://brainly.com/question/29341536

#SPJ4

For l = 3, m = -3, -2, -1, 0, 1, 2, 3, and L2 = m th, the angular momentum can be projected in 7 distinct directions.

As the rotating equivalent of linear momentum in physics, angular momentum (rarely moment of momentum or rotational momentum) is used. It is a conserved quantity, meaning that in a closed system, the total angular momentum stays constant, making it a significant physical quantity. The magnitude and direction of angular momentum are both preserved. The conservation of angular momentum is responsible for the beneficial characteristics of bicycles, motorbikes, frisbees, rifled bullets, and gyroscopes. Hurricanes from spiral galaxies and neutron stars rotate rapidly because of the conservation of angular momentum. Conservation often sets a limit on a system's potential motion but does not determine it in any way.

Learn more about Momentum here:

https://brainly.com/question/24030570

#SPJ4

The light intensity from  largest to smallest ranking will be  :B > D > A=C > E. where the area is measured on the plane perpendicular to the direction .

In physics, the intensity is the amount of energy that is transmitted per unit area, and the area is measured on a plane perpendicular to the direction that the energy equation will propagate. I = P/ 4(d2), with P denoting power. Let power of 1 bulb equal = P where I = intensity, d = distance at which the intensity must be determined.

case A = I =  P / (1) (1) 1 = P case with 2 = P In the situation B = I = 2P/(0.5)2 = 8P C = I = 4P / (2) (2) ^2 = P case Case (1)2 = 3P: D = I = 3P E = I = 2P /(1.5) (1.5) ^2 = 0.8 P

B > D > A=C > E will be the order of light intensity, from greatest to least.

rank the light intensity, from largest to smallest, at the point p in the figures?

learn more about intensity  here:

https://brainly.com/question/13155277

#SPJ4

Lisa can now pick up other paper clips with her freshly magnetized clip after exposing an iron paper clip to a very powerful magnet, which aligns the magnetic domains within the clip.

When a small portion of the iron filings comes into contact with the poles, which are the ends of the magnet, all of the filings are drawn to them. An opposite pole and a similar pole make up a magnet's two poles. While similar poles repel, opposite poles attract. The magnetic force between two magnets increases as the distance between them decreases.

There are three different types of magnets, Permanent magnet, Temporary magnet ,Electromagnets.

When ferromagnetic substances like iron and nickel are exposed to a magnetic field, magnets are produced. When heated to a certain temperature, metals acquire permanent magnetic properties.

To know more about magnetized

https://brainly.com/question/19741986

#SPJ4

The mass varies from only about 100M suns to about 0.08M suns or by about a factor of 1000 along the main sequence, whereas the luminosity varies from 10^6 for the most luminous stars to less than 0.001 or factors of more than 10^9 for the least luminous.

Only the radii of main sequence stars are fairly similar to that of the sun, which implies that the radii change by a smaller factor than the luminosity. The validity of the conclusion can be shown by noting that the luminosity of a star is proportional to R^2T^4, but this is beyond what is covered.

A main-sequence star is a star that burns hydrogen just like the Sun. Massive main-sequence stars are hot and in the upper left of the strip. Low-mass stars have low temperatures and are located in the lower right corner. Massive stars rapidly burn up all their hydrogen in just a few million years. luminosity and distance.

Learn more about Luminosity here:- https://brainly.com/question/6933301

#SPJ4

The displacement is zero because the mass's starting and final positions are identical (it returns to its initial position).

It alludes to the greatest departure from equilibrium that such an object in harmonic oscillator can exhibit. As an illustration, consider how a pendulum moves through its market equilibrium (straight down) and then moves outward to its maximum distance.

The vertical separation of both the wave from average is measured by amplitude. The wave axis, which is typically thought of as zero, is the average size of the wave across one cycle. Positive and negative numbers are assigned to heights between and above the average, accordingly.

To know more about Amplitude visit:

https://brainly.com/question/17003906

#SPJ4

The minimum horsepower must a motor have to be able to drag 310 kg box along a level floor at a speed of 1.20 m/s is 2.199 horse power.

What is called friction?

The resistance to motion of one object travelling in relation to another is referred to as friction. It is not regarded as a fundamental force like gravity or electromagnetic, according to the International Journal of Parallel, Emergent and Distributed Systems(opens in new tab).

First change the mass of 310kg by multiplying by 9.8(gravity), to get 3038 N which equals 'n'

f=μn  =  (.45)(3038)

        = 1367.1N

Use work formula W= fΔx

                              = (1367.1N)(1.2m/s) = 1640.52 Joules/sec

                               (1 Watt = 1 Joules / sec) so you get 1640.52 watts

1 horsepower = 746 watts

1640.52 watt/ 746 watt

= 2.199 horse power

Therefore, the minimum horsepower must a motor have to be able to drag 310 kg box along a level floor at a speed of 1.20 m/s is 2.199 horse power.

To learn more about friction from the given link.

https://brainly.com/question/24338873

#SPJ4

No, the momentum of the block is not conserved.

The block is not isolated—that is, free from outside influences. In actuality, a part of the block's weight force operates in a direction perpendicular to the incline.

Momentum

Momentum is the result of a particle's mass and velocity. Being a vector quantity, momentum possesses both magnitude and direction. According to Isaac Newton's second equation of motion, the force applied on a particle is equal to the time rate of change of momentum.

According to Newton's second law, if a particle is subjected to a constant force for a specific amount of time, the result of the force and time is equal to the change in momentum. On the other hand, a particle's momentum represents the length of time needed for a consistent force to bring it to rest.

Any grouping of particles has a momentum equal to the vector sum of its individual momenta. A change in one particle's momentum is precisely balanced by an equal and opposite change in the momentum of another particle, according to Newton's third law, which states that particles exert equal and opposite forces on one another. The law of conservation of momentum states that when no net external force is acting on a group of particles, their total momentum remains constant.

To know more about Momentum, Check out:

https://brainly.com/question/29113044

#SPJ4

The weight of the ball acting vertically downward is the only force acting on the ball as it moves through the air just leaving the horizontal ramp.

A moving body's force is equal to the product of mass and acceleration. This is the relation stated from Newton's second law of motion. As the mass of the object increases the force that has to be applied on it to change its state will be greater.

The ball which is moving down the horizontal ramp has weight acting downwards. As it is said to ignore air resistance, it can be neglected.

Weight of the ball is nothing but the product of the mass of the ball and acceleration due to gravity.

To know more about force:

https://brainly.com/question/14605963

#SPJ4

The box will be in rest due to net force applied on it is zero.

The definition of force in physics is: The push or pull on a massed object changes its velocity.

An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.

Given that Bert and Ernie are pushing on opposite sides of the box with force of same magnitude, let it be F.

So, net force acting om the force = F-F = 0.

As that net force acting on the box is zero, the box will be in rest.

Learn more about force here:

https://brainly.com/question/13191643

#SPJ1

Yes, the magnitude of the acceleration due to gravity near Earth surface increases more if Earth's mass were doubled.

The magnitude of the acceleration due to gravity on the surface of the Earth is given by the relation,

g = GM/r²

Where,

G is the universal gravitational constant,

M the mass of the earth and,

R is the radius of the earth.

Now if the radius of the earth is kept constant and mass of the earth is doubled.

The value of the new acceleration due to gravity will become,

g' = G2M/r²

Putting GM/r² = g,

g' = 2g

So, we can see that the new acceleration due to gravity because of the increase in the mass of the earth is two times of the earlier acceleration due to gravity.

To know more about acceleration due to gravity, visit,

https://brainly.com/question/88039

#SPJ4

(a) The fraction of neutron's kinetic energy transferred to the atomic nucleus is 0.09.

(b) The final kinetic energy of the neutron is 3.82 x 10⁻¹³ J.

The final velocity of the atom is calculated by applying the principle of conservation of linear momentum as follows;

initial momentum of the neutron = final momentum of the atom

m₁u₁  = m₂u₂

where;

The mass of the atomic nucleus = 11.1 m₁

u₂  = m₁u₁ / m₂

u₂  = m₁u₁ / (11.1 m₁)

u₂  = 0.09u₁

The initial kinetic energy of the neutron is calculated as;

K.Ei = ¹/₂m₁u₁²

The final kinetic energy of the atomic nucleus is calculated as;

K.Ef =  ¹/₂m₂u₂²

K.Ef =  ¹/₂(11.1 m₁)(0.09u₁)²

K.Ef = 0.09 (¹/₂m₁u₁²)

K.Ef = 0.09 (K.Ei)

The fraction of neutron's kinetic energy transferred to the atomic nucleus is calculated as;

= 0.09 (K.Ei) / K.Ei

= 0.09

= 9 %

The final kinetic energy of the neutron is calculated as follows;

K.E.f (neutron) = (1 - 0.09) x (4.2 x 10⁻¹³ J)

K.E.f (neutron) = 3.82 x 10⁻¹³ J

Learn more about final kinetic energy here: https://brainly.com/question/25959744

#SPJ1

Potential difference is the work done in moving a unit charge to a reference point. The potential difference is 9 volts. Thus option B.

Potential difference is a term that is used to describe the work done in transferring a unit positive charge from infinity to a reference point. While the electric field strength is the number of electric field passing through a unit area in a period.

Tension is an example of contact force which is applicable to extended strings, lines, ropes etc.

Given:

electric field strength = 30 V/m

distance between the two points = 30 cm

                                         = 0.3 m

Potential difference between the points = 0.3 x 30

                                          = 9.0 V

Learn more about potential difference at https://brainly.com/question/15278596

#SPJ1

Mechanical waves come in two different varieties: longitudinal waves, in which the medium is moved in the same direction as the wave.

The motion of the wave and the particles is always parallel in longitudinal waves. A classic illustration of a longitudinal wave is a sound wave that is moving through air.

Particles are displaced perpendicular to the wave's direction in a transverse wave. Transverse waves, such as those that cause ripples on the water's surface and vibrations in a string, are examples.

To know more about Mechanical wave visit:-

https://brainly.com/question/24459019

#SPJ4

Charged particles would need to be accelerated by a potential difference of qmv0^2/2 in order to reach the velocity of v0.

The rate at which the charge between two places is exerting work is known as the electric potential difference.

V=W/q is the formula for the electric potential difference.

According to the Work-Energy Theorem, an object's work is equal to the change in kinetic energy.

Relation between Work-Energy Theorem and

Work completed is equal to 1/2MV^2

Considering that the particle's mass is m

Charge of the particle equals q, and particle velocity equals V0.

Work performed on the particle (W) = 0.5 m v 0 2.

Difference in electric potential (V) = W/q

V = 1/2mv0^2 /q

in order for V = qmv0^2/2.

To learn more about potential difference click here https://brainly.com/question/12198573

#SPJ4

a) The speed with which it strikes the ground is 22.212 m/s.

b) It is not influenced by angle and simply relies on mechanical energy conservation.

c) None of the situation would give the higher speed.

Given that,

The height from which the baseball is thrown = 20.8 m

Initial velocity v₀ = 10.6 m/s

Angle = 57.3°

Initially, the potential energy of the ball = m × g × h = m × 9.8 × 20.8 = 204.82 m J

Initial velocity contains two components, vx and vy.

vx = 10.6 cos 57.3° = 5.73

vy = 10.6 sin 57.3° = 8.92

The x component remains constant through the whole motion, so we need to consider the y component only, as the x component will get cancelled as it is same everywhere.

Initially the kinetic energy is,

K.E i = 1/2 m (vy)² = 1/2 m × 8.92² = 39.78 m

Final potential energy = m × g ×h = m × 9.8 ×h

At the height the ball reached, the final kinetic energy is zero.

The conservation of mechanical energy enables us to know that,

P.E i + K.E i = P.E f + K.E f

204.82 m + 39.78 m = m × 9.8 ×h

244.6 = 9.8 ×h

h = 24.96 metres

Now, the potential energy at the highest point is,

P.E f = m × 9.8 × 24.96 = 244.61 m J

Initial kinetic energy was zero, because of the zero speed at the top.

Final kinetic energy will be,

K.E f = 1/2 m × v²

244.61 m = 1/2 m × v²

v² = 244.61 × 2

v = 22.12 m/s

b) If the ball would have been thrown at an angle of 57.3°, below the horizontal, then also the final velocity would be 22.12 m/s. It is not influenced by angle and simply relies on mechanical energy conservation.

c) The air resistance will produce a decrease in the final speed.

We know that friction is a non conservative force and our system will become a dissipative system as the total mechanical energy would not be conserved.

Air friction will cause a decrease in speed. None of the situation would give the higher speed.

To know more about mechanical energy:

https://brainly.com/question/15062290

#SPJ4

1. The equivalent emf of the collection is 15.6 V

2. The current through the resistor is 4.7 A

1. How do I determine the equivalent emf?

The equivalent emf of the collection can be obatined as illustrated below.

The following were obtained from the question:

E = E₁ + E₂ + E₃ + E₄ + E₅

E = 3 + 4.5 + 1.5 + 2 + 4.6

E = 15.6 V

Thus, the equivalent emf is 15.6 V

2. How do I determine the current ?

The current through the resistor can be obtained as follow:

Emf (E) = Current (I) × resistance (R)

15.6 = Current × 3.3

Divide both sides by 3.3

Current = 15.6 / 3.3

Current = 4.7 A

Thus, the current is 4.7 A

Learn more about current:

https://brainly.com/question/23754329

#SPJ1

Complete question:

See attached photo

A 1200 kg SUV will take 1875.6 N of net force to accelerate it across 200 meters at 25 m/s from a standstill.

Where:

a = acceleration (m/s²)

v = final velocity (m/s)

u = initial velocity (m/s)

s = distance (m)

v² - u² = 2as

a = v² - u²/2s

a = 25² - 0²/2(200)

a = 625/400

a = 1.563m/s²

Since a = 1.563m/s²

F = 1200 × 1.563

F = 1875.6N

Therefore, a 1200 kg SUV will need to accelerate with a net force of 1875.6 N over a 200 m distance to reach a speed of 25 m/s.

In mechanics, a force is any action that has the potential to change, maintain, or deform a body's motion. The three principles of motion outlined by Isaac Newton in his Principia Mathematica are frequently used to illustrate the concept of force (1687). Newton's first law states that a body at rest or moving uniformly in a straight line will stay in that state until a force is applied to it. According to the second law, a body will accelerate (change in velocity) in the direction of any external force acting on it. The amount of acceleration is directly related to the amount of external force.

Learn more about force here:

https://brainly.com/question/28875770

#SPJ4

In the cores of main sequence stars, hydrogen atoms are fused to form helium atoms. The sun is one of the majority of main sequence stars, which make up about 90% of all stars in the universe.

These stars can be as much as 200 times as massive than the sun or only a tenth as massive.

Stars begin their lives as gas and dust clouds. These clouds are brought together by gravity. The falling material acts as the fuel for a tiny protostar. Protostars can be difficult to find and frequently form in tightly packed gas clouds.

Mark Morris of the University of California, Los Angeles (UCLS), stated in a statement that "Nature doesn't generate stars in solitude" (opens in new tab). "It creates them in groups from natal clouds that burst under.

Therefore, In the cores of main sequence stars, hydrogen atoms are fused to form helium atoms. The sun is one of the majority of main sequence stars, which make up about 90% of all stars in the universe.

To learn more about Sun, refer to the link:

https://brainly.com/question/17376727

#SPJ1

This mosaicism in Turner's syndrome develops as a result of some cells in an XY embryo rapidly losing a Y chromosome after fertilization.

The zygote will have karyotype 44+XY if the sperm contains a Y chromosome. A gamete with the X chromosome will be produced by a mother. The resulting embryo would be a 44+XY (total 46 chromosomes). This zygote begins to divide its cells, but if the embryo's cells somehow lose the Y chromosome, the karyotype will change to 44+X0 (totaling 45 chromosomes, which is the Turner's syndrome disease).

Thus, certain cells that were originally destined to create an XY embryo with 46 chromosomes now have 45 chromosomes and the Turner's syndrome X0 condition.

To know more about Turner's syndrome

https://brainly.com/question/29486877

#SPJ4

Answer: (option b) on the equator only on the March and September equinoxes

Explanation:One of the abecedarian data of life at Earth’s midlatitudes, where utmost of this book’s compendiums live, is that there are significant variations in the heat we admit from the Sun during the course of the time. We therefore divide the time into seasons, each with its different quantum of sun. The difference between seasons gets more pronounced the further north or south from the ambit we travel, and the seasons in the Southern Hemisphere are the contrary of what we find on the northern half of Earth. With these observed data in mind, let us ask what causes the seasons.

numerous people have believed that the seasons were the result of the changing distance between Earth and the Sun. This sounds reasonable at first it should be colder when Earth is further from the Sun. But the data do n’t bear out this thesis. Although Earth’s route around the Sun is an cirque, its distance from the Sun varies by only about 3. That’s not enough to beget significant variations in the Sun’s heating. To make matters worse for people in North America who hold this thesis, Earth is actually closest to the Sun in January, when the Northern Hemisphere is in the middle of downtime.



To know more about zeinith visit

https://brainly.com/question/19505412

The Sun reaches the zenith (directly overhead) at midday on the equator every day. Therefore, option D is correct.

The relationship between the Sun and the equator also affects the seasons. As the Earth orbits the Sun, its axial tilt causes different parts of the Earth to receive varying amounts of sunlight throughout the year. When the Sun is directly overhead at the Tropic of Cancer during the June solstice, it marks the start of summer in the Northern Hemisphere and winter in the Southern Hemisphere.

Conversely, when the Sun is directly overhead at the Tropic of Capricorn during the December solstice, it marks the start of summer in the Southern Hemisphere and winter in the Northern Hemisphere.

Learn more about the equator, here:

https://brainly.com/question/32435279

#SPJ2

Due to its dependence on L, the spacings between various fringes get smaller as the distance between the slits gets more. The space between various fringes grows as the light's wavelength rises because this is a wavelength-dependent property.

Distance between the core bright fringe and two side-by-side dark fringes is 2 mm (1. 2 inches).

As a result, "xn = (2n+1)D/2d" is how far the "n" brilliant fringe is from the "centre." Similar to the example above, the formula for the distance between the "n-1" dark fringe and the "centre" is: "x (n-1)= (2(n-1) +1)D/2d."

To know more about interference  visit:-  

https://brainly.com/question/16098226

#SPJ4

You would alter the separation width and track the system's diffraction angle to verify this theory. Therefore, the Gap Width is the variable and the Diffraction Angle would serve as the dependent variable.

Salt will become more soluble as even the temperature rises. UV radiation exposure is associated to the risk of skin cancer. Many brands of light bulbs have the same lifespan. Cats don't care what color their cat chow is.

A great hypothesis statement includes a prediction, is unambiguous and testable. While "testable" denotes verifiability or falsifiability, it also implies that you may conduct the required tests without going against any ethical norms.

To know more about Hypothesis  visit:

https://brainly.com/question/10854125

#SPJ1

The complete question is-

The goal of this experiment was to answer the question, "How does diffraction occur?" Suppose you formulated this alternate hypothesis:

If the gap width is increased while keeping wavelength constant, then the observed diffraction will decrease because the less the ratio between wavelength and gap width is, the smaller the observed diffraction angle will be.

To test this hypothesis, you would change the and observe the in the system.

Therefore, the independent variable would be the and the dependent variable would be the .

1. is gap width

2. is diffraction angle

3. is gap width

4. is diffraction angle

Explanation:

The different component of the momentum of the ball is as bellow,

As per the details share in the above question are s bellow,

The mass of the super ball m is =50gm

The super ball drop from the height of = 1.5 m

Consider the ball's speed be v right before it hits the table.

Decrease of Potential Energy = Increase of Kinetic Energy

=> m x 9.8 x 1.5 = [tex]0.5 m v^{2}[/tex]

=> Therefore velocity = 5.42 m/s (- y direction)

A) Prior to a collision, the momentum component Y = mv

= - 0.05 x 5.42 = - 0.271 kg m/s

Consider the ball's speed be u right before it hits the table.

Increase of PE = Decrease of KE

=> m x 9.8 x 1 = [tex]0.5 m u^{2}[/tex]

=> u = 4.427 m/s (+ y direction)

B) Following the impact, the ball's Y contribution of momentum = mu

= 0.05 x 4.427 = 0.221 kg m/s

C) Now when Impulse imparted,

Consider Jy = change in momentum

= 0.221 - (-0.271) = 0.492 kg m/s

D) The ball time of contact is = 15 ms

Force = change inimpulse / time

= 0.492/0.015 = 32.82 N

E) change in Kinetic energy during collision

= KE after - KE before

[tex]= 0.5 \times 0.05 \times 4.427^{2} - 0.5\times0.05\times5.42^{2}[/tex]

= - 0.24445 J

For more such question on kinetic energy.

https://brainly.com/question/25959744

#SPJ4

Note: The correct correct question would be as bellow,

As shown in the figure (Figure 1) , a superball with mass m equal to 50 grams is dropped from a height of hi=1.5m . It collides with a table, then bounces up to a height of hf=1.0m . The duration of the collision (the time during which the superball is in contact with the table) is tc=15ms . In this problem, take the positive y direction to be upward, and use g=9.8m/s2 for the magnitude of the acceleration due to gravity. Neglect air resistance.

A) Find the y component of the momentum Pbefore,y of the ball immediately before the collision (in kg x m/s)

B) Find the y component of the momentum of the ball immediately after the collision, that is, just as it is leaving the table (in kg x m/s)

C) Find Jy, the component of the impulse imparted to the ball during collision (in kg x m/s)

D) Find the y component of the time-averaged force Favg,y in Newtons, that the table exerts on the ball

E)Find Kafter - Kbefore, the change in the kinetic energy of the ball during the collision, in Joules.

The time period of oscillation is 1.84 s.

Simple pendulum's time period is nothing but the time taken to complete one oscillation. It is measured in seconds and minutes.

Given that, length of the uniform rod = 0.85 m

We know the expression for time period as,

T = 2π√(l/g)

where, T is time period

l is length

g is acceleration due to gravity

Substituting the values in the above equation, we have

T = 2π√(l/g) = 2π* √(0.85/10) = 2π* 0.292 = 1.84 s

Thus, the time period of oscillation is found to be 1.84 s.

To know more about time period:

https://brainly.com/question/12903836

#SPJ4

Manometer-style pressure gauges have a small, liquid-filled U-shaped tube inside.

Reading the marks on this tube will tell you how pressurized your system is. When pressure is applied to either side of the gauge, the water in the tube rises in one direction or the other. The most important kinds of pressure measurements use atmospheric pressure as their standard. When a tire is inflated to 30 psi, for instance, a standard tire pressure gauge will display this number as 30 psig (the "g" stands for gauge pressure). The liquid fill makes pressure measurements simpler by attenuating vibration, mechanical stress, and pressure pulsations. Due to the ambient atmosphere, the liquid fill prevents corrosion, moisture infiltration, and ice.

Learn more about pressure here-

https://brainly.com/question/29341536

#SPJ4

the buoyant force on the ball is 4 N

buoyant force formula,

Fb=-ρgV

To calculate the buoyant force, the formula can be used: Fb=ρVg Fb = ρVg where Fb is the buoyant force in Newtons, ρ is the density of the liquid in kilograms per cubic meter, and V is the displaced volume of liquid in cubic metres. ), g is the gravitational acceleration

Buoyancy is the upward force on an object that is wholly or partially immersed in liquid. This upward force is also called thrust. Buoyancy causes a body that is wholly or partially immersed in liquid to appear weighed down. H. Easier

Learn more about buoyant force here : https://brainly.com/question/28184066

#SPJ4

A waterskier skis over the ramp shown in the figure at a speed of 30 ft/s, 7.73 ft/sec is rising as she leaves the ramp.

We assume the hypotenues = h

From the given figure (attached) ;

h² = x² + y²

Put the  values of x and y from the figure

h² = 15² + 4²

h² = 225 + 16

h² = 241

Take under root on both sides

h = √241

From the figure the value of sin∅ = 4/h

Put value of h

sin∅ = 4 / √241

The rate at which she is rising = verticle velocity

The rate at which she is rising = 30sin∅

Put the value of sign∅

The rate at which she is rising = (30 * 4) / √241

The rate at which she is rising = 7.73 ft/sec

The missing figure is attached.

You can also learn about verticle velocity from the following question:

https://brainly.com/question/29553099

#SPJ4