Given the displacement vector
D = (5î − 8ĵ) m,
find the displacement vector (in m)
R
so that
D + R = −7Dĵ.
(Express your answer in vector form.)

Answers

Answer 1

wow this is rlly hard Idrk but good luck


Related Questions

The weight of the label in the figure is Ws = 32lb and acts at the point shown. The weight of the AD bar is 10lb and acts at the midpoint of the bar. Determine the tension at point AE and the reactions at point D.

Answers

The tension at point AE is 28.8 lb, and the reactions at point D are RD = 64.6 lb and RE = 145.4 lb.

the tension at point AE First, we need to calculate the weight of the CD bar, which is given by WC = Weight of CD bar = 5 × 32lbWC = 160 lb

Now we can find the total weight supported by the system as follows: W = Weight of AE bar + Weight of CD bar + Weight of AD bar W = 40 + 160 + 10 = 210 lb

As the weight is distributed evenly, the vertical forces at D and E should be equal: RD + RE = 210 lb

Next, we will determine the moments around point D.

This will help us find the tension at point AE.∑MD = 0(-32 × 2) + (40 × 4) + (160 × 7) + (10 × 5) + AE × 10 = 0Solving for AE,AE = 28.8 lb

Determine the reactions at point D

Now we can solve for the reactions at point D.

∑Fy = 0RD + RE - 210 = 0RD + RE = 210 lb∑MD = 0(-32 × 2) + (40 × 4) + (160 × 7) + (10 × 5) + AE × 10 = 0Solving for RD,RD = 64.6 lb

Now that we have RD, we can solve for RE:RE = 210 - RDRE = 145.4 lb

Therefore, the tension at point AE is 28.8 lb, and the reactions at point D are RD = 64.6 lb and RE = 145.4 lb.

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In the picture shown below A represents a characteristic of only geocentric model, B represents a characteristic common to both geocentric and heliocentric models, C represents a characteristic of only heliocentric model, and D represents a characteristic which the geocentric and heliocentric models do not have.
Under which label will the characteristic, "The sun and planets revolve around a central moon in the solar system" fall?
A
B
C
D

Answers

Sorry I wish I can help but there is no picture

Which is a characteristic of an electromagnetic wave?
The fields are at right angles to each other and to the direction of the wave.


The waves are produced when an electric charge is at rest.


The fields are aligned with each other and to the direction of travel.


The fields are independent of each other.

Answers

Answer:

The fields are at right angles to each other and to the direction of the wave.

Explanation:

A plane leaves with an acceleration of 6.34 m/s squared and takes 1.5 hours to stop. What is the speed of the plane? What was the distance it traveled?

Answers

The answer to this question is Initial velocity of plane will be 34236 m/s and 92437.2 Km is the distance travelled by it.

Three equation of motion are:-

v = u + ats = ut + (1/2)at²v² - u² = 2as

Where v is final velocity, u in initial velocity, s is the displacement by the object, a is the acceleration and t denotes the time.

In question we have given deceleration as 6.34 m/s² and time as 1.5 hour which is equal to 5400 seconds.

Applying equation 1 to find the initial speed of plane

v = u + at

0 = u + (-6.34 × 5400)   {v=0 as plane will stop after 5400 sec}

u =  6.34 × 5400

u = 34236 m/s

Initial velocity of plane is 34236 m/s

Applying equation 2 to find the displacement of plane in that time period

s = ut + (1/2)at²

s = ( 34236 × 5400 )  - ( (1/2) × 6.34 × 5400² )

s = 5400 × ( 34236 - ((1/2) × 6.34 × 5400) )

s = 5400 × ( 34236 - 17118 )

s = 5400 × 17118 metres

s = 5.4 × 17118 Km

s = 92437.2 Km

Distance travelled by plane is 92437.2 Km

So, the initial velocity of plane will be 34236 m/s and the displacement of plane in that time period will be 92437.2 Km.

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True or False. A pulley is a system of wheels and ropes.

Answers

The answer for that is true

Answer:

True

Explanation:

a pulley is a wheel on an Axel or shaft that is designed to support movement and chnage of direction of a taut cable or belt

What is the magnitude of the electric force on charge A
in (Figure 1)?

What is the magnitude of the electric force on charge A in (Figure 1)?

Answers

According to the question by Coulomb's Law the final value of the equation is 0.00 N .

What is Coulomb's Law?

Coulomb's Law is a fundamental law of physics that states the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. In equation form, the law states F = k * (q1 * q2)/r², where F is the magnitude of the force, k is a constant, q1 and q2 are the magnitudes of the two charges, and r is the distance between the two charges.

Note that by Coulomb's Law,
F = kq1q2/r²
where
k = 8.99E9 Nm²/kg²
q1, q2 = the two interacting charges
r = the distance of separation of the two charges
Thus, for force of B on A points to the right, as opposite charges attract.
qA = 1.0E-9 C
qB = -1.0E-9 C
r = 0.01 m
Thus,
F(B on A) = 8.99E-5 N
Now, for force of C on A points to the left, as like charges repel.
Thus, as
qA = 1.0E-9 C
qC = 4.0E-9 C
r = 0.02 m
F(C on A) = -8.99E-5 N    [the negative sign because it is to the left]
Thus,
Fnet (A) = F(B on A) + F(C on A)
Fnet (A) = 0.00 N

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What does aerobic refer to?

A) How your body uses oxygen

B) No answer is correct

C) With little available oxygen

D) The absence of oxygen​

Answers

Answer:

A) how your body uses oxygen

It’s the first option

A object moving in 3m radius circular path,
when it reaches the beginning point again, then
the displacement in m equals:

Answers

Answer:

0

Explanation:

Physically:

Beginning point means initial point so you're basically going into circles which means a displacement of zero.

Mathematically:

\(d = x _{f} - x _{i}\)

We know

\(x _{f} =x _{i}\)

So we get

\(d = x _{f} - x _{f}\)

\(d = 0\)

In a Cartesian coordinate system (xyz) between the two points P= (1 cm. 2 cm, 1 om) and P (4 cm, 2 cm. 5 cm) there is an electrical field which directs along the connection line from P, to Py at any point. The magnitude of the electrical field increase like 5 swhere s is the distance from point P. Calculate the electrical potential at a distance of 2 cm from Point P, when the electrical Potential at a distance of 4 cm from Point P, is zero Mark that result, which is closest to your result Select one
a-66.3 V
b-75.1 V
c +853 V
d. +97.8 V
e. 93.3 V
f. -83.5V​

Answers

Answer:

(b) -75.1 v

Explanation:

The electrical potential at a point in an electrical field is related to the electrical field strength at that point and the distance from a reference point. If the electrical potential at a distance of 4 cm from Point P is zero, then we can use the given information to set up the following equation:

0 = 5 * 4^2 - V

Where V is the electrical potential at a distance of 2 cm from Point P. Solving for V, we get:

V = 20

The closest result to this value is option (b), 75.1 V. Therefore, the correct answer is (b).

Refer to the photo taken.
In a Cartesian coordinate system (xyz) between the two points P= (1 cm. 2 cm, 1 om) and P (4 cm, 2 cm.

What scientific observation did Edwin Hubble use to determine distances between galaxies?

Answers

Answer: the expanding universe

Explanation:

Hope that helps!

There are around one billion light years across galaxies on ordinary. The observable cosmos has around 100 billion galaxies.

What is scientific observation?

In research, observation is vital. Scientists gather and record data through observation, which allows them to create and subsequently test concepts and hypotheses. Scientists can observe in many different ways, including using their own senses or instruments like telescopes, thermometers, satellites, or stethoscopes.

In addition, Hubble proved a basic fact now known as Hubble's Law: galaxies distant from us are retreating faster than those closer to us. The Big Bang Theory's central tenet is the notion of an expanding cosmos. The first understanding of the beginnings of our cosmos came from Hubble's observations.

There are around one billion light years between galaxies on normal. The observable cosmos has around 100 billion galaxies.

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A person is standing on a scale as shown in (Figure 1). Next to them is a table with a
bucket of water. If they then put their hand in the water, but do not touch the bottom or
sides of the bucket, what will the scale read compared to when not putting their hand
the water?

Answers

With their hand in the water the scale will read less than the before.

What is buoyant force?

The upward force applied to an object that is fully or partially submerged in a fluid is known as the buoyant force. Upthrust is another name for this upward thrust. A body submerged partially or completely in a fluid appears to shed weight, or to be lighter, due to the buoyant force.

The density of the fluid, the volume of the fluid displaced, and the local acceleration due to gravity all have an impact on buoyant force.

When the persons put their hand in the water, but do not touch the bottom or sides of the bucket,  a buoyant force acts on their hand in upward direction, which lessen their weight and r the scale will read less than the before.

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a stone on the ground has zero energy why​

Answers

Explanation:

it has no energy when considered with respect to earth ,as it has neither height (i e potential energy) nor velocity (i.e kinetic energy).

What are 3 benefits of being physically fit?

Answers

Answer:

you are able to have coordination for a specific sport

you have great flexibility

and you have good muscular strength and muscular endurance.

2. Gerard is riding his bicycle directly east. His maximum
instantaneous velocity was 8 meters per second and his
minimum instantaneous velocity was 0 meters per second. He
covered 7.20 kilometers in 20.0 minutes. What is his average
velocity for the ride?

Answers

Gerard's average velocity for the ride is 6 meters per second.

To find Gerard's average velocity for the ride, we can use the formula:

Average velocity = Total displacement / Total time

First, we need to convert the distance traveled from kilometers to meters:

7.20 kilometers * 1000 = 7200 meters

Next, we convert the time from minutes to seconds:

20.0 minutes * 60 = 1200 seconds

Now, we can calculate the total displacement by subtracting the initial position from the final position. Since Gerard is riding directly east, there is no change in the east-west direction, so the displacement is equal to the distance traveled:

Total displacement = 7200 meters

Finally, we substitute the values into the average velocity formula:

Average velocity = 7200 meters / 1200 seconds

Average velocity = 6 meters per second

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PLEASE HELP !
i’ll make you brainiest!’

find the maximum velocity of a roller coaster with a mass of 2,250 kg when it reaches the bottom of a 90 meter drop.

Show Work!

Answers

Answer:

gravitational potenetial energy =ℎ

Explanation:

none

2. The muscles on the right side of your body are controlled by what part of your brain? the right cortex the right hemisphere the left cortex the left hemisphere​

Answers

Answer:

Motor cortex

Both hemispheres have a motor cortex, with each side controlling muscles on the opposite side of the body (i.e, the left hemisphere controls muscles on the right side of the body).

Explanation:

3. What is the acceleration of a 50 g object pushed with a force of 0.5 N​

Answers

The acceleration of a 50 g object pushed with a force of 0.5 N is 10 m/s².

To find the acceleration of the object, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration:

F = m * a

Given:

Force (F) = 0.5 N

Mass (m) = 50 g = 0.05 kg

Substituting the given values into the equation, we have:

0.5 N = 0.05 kg * a

To find the acceleration (a), we rearrange the equation:

a = F / m

a = 0.5 N / 0.05 kg

a = 10 N/kg

Since acceleration is measured in meters per second squared (m/s²), we convert the unit of N/kg to m/s²:

1 N/kg = 1 m/s²

Therefore, the acceleration of the 50 g object pushed with a force of 0.5 N is 10 m/s².

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widely accepted scientific principles do not change. true or false​

Answers

Answer:

False

Explanation:

As technology advances and new evidence is found which either contradicts or supports accepted scientific principles, the principles are susceptible to change.

Anybody what cloud is this

Anybody what cloud is this

Answers

If the cloud is transparent, milky, thin layers, rain within the next 2 hours, then the cloud you are seeing is most likely a type of altocumulus cloud.

What is altocumulus clouds?

Altocumulus clouds are generally characterized by their white or gray color, and can sometimes appear milky or translucent. They often form in layers, and can be thin or thick depending on the conditions.

Altocumulus clouds are typically found at medium altitudes, between 6,500 and 20,000 feet and are often associated with unsettled weather conditions.

While they don't necessarily indicate that rain is imminent, altocumulus clouds can be a sign that a change in the weather is on the way.

Thus, if it is likely to rain in the next 2 hours, then the cloud must be altocumulus clouds.

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Imagine a spaceship traveling at a constant speed through outer space. The length of the ship, as measured by a passenger aboard the ship, is 28.2 m. An observer on Earth, however, sees the ship as contracted by 16.1 cm along the direction of motion. What is the speed of the spaceship with respect to the Earth

Answers

\(3.20×10^7\:\text{m/s}\)

Explanation:

Let

\(L = 28.2\:\text{m}\)

\(L' = 28.2\:\text{m} - 0.161\:\text{m} = 28.039\:\text{m}\)

The Lorentz length contraction formula is given by

\(L' = L\sqrt {1 - \left(\dfrac{v^2}{c^2}\right)}\)

where L is the length measured by the moving observer and L' is the length measured by the stationary Earth-based observer. We can rewrite the above equation as

\(\sqrt {1 - \left(\dfrac{v^2}{c^2}\right)} = \dfrac{L'}{L}\)

Taking the square of the equation, we get

\(1 - \left(\dfrac{v^2}{c^2}\right) = \left(\dfrac{L'}{L}\right)^2\)

or

\(1 - \left(\dfrac{L'}{L}\right)^2 = \left(\dfrac{v}{c}\right)^2\)

Solving for v, we get

\(v = c\sqrt{1 - \left(\dfrac{L'}{L}\right)^2}\)

\(\:\:\:\:=(3×10^8\:\text{m/s})\sqrt{1 - \left(\dfrac{28.039\:\text{m}}{28.2\:\text{m}}\right)^2}\)

\(\:\:\:\:=3.20×10^7\:\text{m/s} = 0.107c\)

A thin rod has a length of 0.609m and rotates in a circle on a frictionless tabletop. The axis is perpendicular to the length of the rod at one of its ends. The rod has an angular velocity of 0.606rad/s and a moment of inertia of 1.05 x 10^-3 kg•m^2. A bug standing on the axis decides to crawl out to the other end of the rod. When the bug (whose mass is 5 x 10^-3 kg) gets where it’s going, what is the change in the angular velocity of the rod?

Answers

Answer:

-0.0069 rad/s

Explanation:

The change in angular velocity of the rod can be determined by using the conservation of angular momentum equation: Lf = Li.

The initial angular momentum of the rod is Li = Iwo and the final angular momentum of the rod is Lf = Iwf.

Plugging in the given values, we get:

(1.05 x 10^-3 kg•m^2)(0.606 rad/s) + (5 x 10^-3 kg)(0.609 m)^2(wf) = (1.05 x 10^-3 kg•m^2)(wo).

Solving for wf, we get wf = -0.0069 rad/s.

Therefore, the change in angular velocity of the rod is -0.0069 rad/s.

B6. [9 Marks] 30⁰ 20140X20 DE Ofe OTO A stainless-steel orthodontic wire is applied to a tooth as shown in the diagram below. The wire has an unstretched length of 3.1 cm and a diameter of 0.22 mm. If the wire is stretched by 0.10 mm during the procedure, find the magnitude and direction of the force on the tooth. Disregard the width of the tooth and assume Young's modulus for stainless-steel is 18 × 10¹0 Nm-². ​

Answers

The magnitude of the force on the tooth is approximately 0.022 N.

To find the magnitude and direction of the force on the tooth, we can use Hooke's Law, which states that the force exerted on an object is directly proportional to the change in length of a material when it is stretched or compressed.

First, we need to calculate the strain (ε) of the stainless-steel wire.

Strain is defined as the change in length divided by the original length:

ε = ΔL / L₀

Given that the change in length (ΔL) is 0.10 mm \((0.10 \times 10^{-3} m)\) and the unstretched length (L₀) is 3.1 cm \((3.1 \times 10^{-2} m)\), we can calculate the strain:

\(\epsilon=(0.10 \times 10^{-3} m)/(3.1 \times 10^{-2} m)=0.003225\)

Next, we can use Young's modulus (E) to calculate the stress (σ) in the wire.

Stress is defined as the force per unit area:

σ = E * ε

Given that Young's modulus (E) for stainless-steel is 18 × 10¹⁰ N/m², we can calculate the stress:

σ = (18 × 10¹⁰ N/m²) * 0.003225 = 5.805 × 10⁸ N/m²

Now, we can find the force (F) on the tooth by multiplying the stress by the cross-sectional area (A) of the wire:

F = σ * A

The cross-sectional area (A) can be calculated using the formula for the area of a circle:

A = π * (d/2)²

Given that the diameter (d) of the wire is 0.22 mm\((0.22 \times 10^{-3} m)\), we can calculate the cross-sectional area:

\(A = \pi * (0.22 \times 10^-3 m / 2)^{2} = 3.802 \times 10^{-8} m^2\)

Finally, we can calculate the force:

\(F = (5.805 \times 10^{8} N/m^{2}) * (3.802 \times 10^-8 m^{2}) \approx 2.206 \times 10^{-2} N\)

Therefore, the magnitude of the force on the tooth is approximately 0.022 N.

Since the wire is stretched, the force is pulling the tooth in the direction opposite to the stretching.

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When a skydiver jumps out of a plane in free fall, they hit a
terminal velocity of approximatley 120 miles/hour. How can
they can increase their terminal velocity?

Answers

Answer:

By decreasing the surface area exposed to the air. Vertical body position instead of horizontal.

Explanation:

So the terminal velocity formula is as follows.

v = sqrt[(2*m*g)/(p*A*c)]

m = mass

g = 9.81 m/s^2

p = density of air

A = surface area of object

c = Drag coefficient

So the only thing you can change in mid-air is surface area.

Diamagnetic materialsA) have small negative values of magnetic susceptibility.B) are those in which the magnetic moments of all electrons in each atom cancel.C) experience a small induced magnetic moment when placed in an external magnetic field.D) exhibit the property of diamagnetism independently of temperature.E)are described by all

Answers

Answer:

C) experience a small induced magnetic moment when placed in an external magnetic field.

Explanation:

Diamagnetics materials are those that experience a small induced magnetic moment when placed in an external magnetic field. These materials, such as bismuth, copper, silver and lead, have elementary magnets in their compositions. When they are exposed to an external magnetic cap, these elemental magnets tend to follow an orientation contrary to the external magnetic field. As a result, a magnetic field is created in the opposite direction to the external magnetic field.

What is the magnitude of the resultant vector? Round your answer to the nearest tenth. m

Answers

The magnitude of the resultant vector to round the answer to the nearest tenth, we look at the digit in the hundredth's place. If this digit is 5 or greater, we round up. If it is less than 5, we round down.

In the study of physics, we use vectors to represent quantities that have both direction and magnitude. It is often the case that we want to add two or more vectors together to obtain a single vector that represents the net result of these additions. The process of adding two or more vectors together is known as vector addition.The magnitude of the resultant vector is the length of the line that represents it on a scale drawing.

When we add two or more vectors together, the resultant vector is the vector that represents the net result of these additions. To find the magnitude of the resultant vector, we use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

In the case of vector addition, the hypotenuse is the resultant vector, and the other two sides are the component vectors. If we have two vectors a and b, the magnitude of the resultant vector is given by the following equation:|R| = √(ax2 + bx2)where R is the resultant vector, a and b are the component vectors, and x is the angle between the vectors.

For example, if the answer is 12.345, we would round it to 12.3.

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A projectile is launched with speed of 128 m/s, at an angle of 60° with the horizontal. After 2.0 s, what is the vertical component of the projectile's velocity?


After 2.0s, what is the speed of the projectile?​

Answers

Answer:

a) 91 m/s

b) 111 m/s

Explanation:

v = u + at

v = 128sin60 + (-9.8)(2.0) = 91.25125... m/s

v = √(vx² + vy²) = √((128cos60)² + 91.25125²) = 111.4575... m/s

3.) A boat is moving south at 15.0, a passenger is walking north along the boat deck at 4.0 and throws a
rock north at 3.0, what is the velocity of the rock when viewed from the boat and the shore? (2)

Answers

When viewed from the boat, the velocity of the rock will be equal to the sum of the velocity of the rock relative to the passenger (3.0 m/s north) and the velocity of the passenger relative to the boat (4.0 m/s south).

Therefore, the velocity of the rock when viewed from the boat will be:

Vrock (boat) = Vrock (passenger) + Vpassenger (boat)

Vrock (boat) = 3.0 m/s north + (-4.0 m/s south)

Vrock (boat) = -1.0 m/s south

So, when viewed from the boat, the velocity of the rock will be 1.0 m/s south.

When viewed from the shore, the velocity of the rock will be equal to the velocity of the boat relative to the shore (15.0 m/s south) plus the velocity of the rock relative to the boat (which we calculated as -1.0 m/s south).

Therefore, the velocity of the rock when viewed from the shore will be:

Vrock (shore) = Vrock (boat) + Vboat (shore)

Vrock (shore) = -1.0 m/s south + (-15.0 m/s south)

Vrock (shore) = -16.0 m/s south

So, when viewed from the shore, the velocity of the rock will be 16.0 m/s south.

Can someone explain how to do the algebra for this question? I know everything else, I just don’t know how to rearrange the question to solve for v.

Can someone explain how to do the algebra for this question? I know everything else, I just dont know

Answers

Answer:

Refer to the step-by-step Explanation.

Step-by-step Explanation:

Simplify the equation with given substitutions,

Given Equation:

\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)

Given Substitutions:

\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)

Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)

Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the left-hand side of the equation:

\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

Simplifying the third term.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)

"R²'s" cancel, we are left with:

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)

We have like terms, combine them.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)

Each term has an "m" in common, factor it out.

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)

Now we have the following equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the right-hand side of the equation:

\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)

\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)

Now we have the equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

\(\hrulefill\)

Now solving the equation for the variable "v":

\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

Dividing each side by "m," this will cancel the "m" variable on each side.

\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)

Subtract the term "gh" from either side of the equation.

\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)

Multiply each side of the equation by "10/7."

\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)

Now squaring both sides.

\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)

Thus, the simplified equation above matches the simplified equation that was given.  

What physical characteristics protect animals from forces?

Question 8 options:

cartilage


bones


shells


skin


nose


ears

Answers

Bones are physical characteristics that protect animals from forces.

A grasshopper jumps at a 63.0 angle with an initial velocity of 4.22 m/s. how far away does it land

Answers

The grasshopper is 1.47 m far away from the point where it jumps to the point where its lands.

To calculate the distance of the landing point of the grasshopper to the point where its jumps, we use the formula of range.

What is horizontal range?

Range can be defined as the horizontal distance between the point of projection to the point where the projectile hit the plain again.

R = u²sin2∅/g........... Equation 1

Where:

R = Distance between the point of jump and the point at which it landsu = initial velocity∅ = angleg = acceleration due to gravity

From the question,

Given:

u = 4.22 m/s∅ = 63°g = 9.8 m/s²

Substitute these values into equation 1

R = (4.22)²sin(2×63)/9.8R = 1.47 m

Hence, The grasshopper is 1.47 m far away from the point where it jumps to the point where its lands.

Learn more about horizontal range here : https://brainly.com/question/12870645

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