A toy rocket with a mass of 300 g takes off in a vertical direction under the influence of gravity. It burns fuel at the rate of 25 g/s. The exhaust speed of the gases is 80 m/s. What is the speed of the rocket at the end of 10 seconds

Answer:

The angle of launch is 52.49 Degree.

Explanation:

The Range R and Height H of a thrown object is calculated using the formula,

R=V₀² sin(2φ)/g

H=V₀²sin²(φ)/g

From these equations it can be written,

V₀²=R g/ sin(2φ)

V₀²=H g/ sin²(φ)

These values are equal so it can be written by equating these equations,

R g/sin(2φ)=H g/sin²(φ)

tan(φ)= 2H/R

Given H=72.3 m and R=111 m, the angle of launch is,

tan(φ)= 2*72.3/111

φ= 52.49 Degree.

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Imagine that a star-forming cloud collapses but retains all of its mass in a single blob. In order to conserve angular momentum, the cloud must spin faster.

Conservation of angular momentum is a physical characteristic of a rotational system that keeps its rotation constant unless it is affected by an external torque. In other words, the speed is constant as long as the net torque is zero.

In angular kinematics, conservation of angular momentum refers to the tendency of the system to preserve angular momentum in the absence of external torque. If the objects collide without net external torque, the angular momentum is constant. The two objects exert equal but opposite angular momentums to maintain the full angular momentum of the colliding system.

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The stone will strike the ground with velocity of 33.5 m/s.

What is velocity:

What is displacement:

Here,

Stone is dropped freely from rest, so it's Initial velocity will be zero.

u = 0 m/s

displacement is equal to half of total height.

y = h/2

since Stone is dropped freely, a=g ( acceleration of gravity)

According to Newton's equation of motion:

y = u* t + 1/2 (at^2)

h/2 = 0 + 1/2 (gt^2)

h = g* t^2 -----1

now at t= t+1 , displacement y = h

h = u* t + ½ g (t + 1)²

h = ½ g (t + 1)² -----2

comparing both equations,

g* t^2 = ½ g (t + 1)²

2t² = (t + 1)²

2t² = t² + 2t + 1

t² − 2t = 1

t² − 2t + 1 = 2

(t − 1)² = 2

t − 1 = ±√2

t = 1 ± √2

Since t > 0, t = 1 + √2.  

So t+1 = 2 + √2.

At that time, the speed is:

v = at + u

v = g (2 + √2) + 0

v = g (2 + √2)

If g = 9.8 m/s²,

v = 33.5 m/s.

The stone will strike the ground with velocity of 33.5 m/s.

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Answer:

The current in a circuit can be determined as total amount of charge passes through a wire's full cross section area.

Explanation:

The current is a flow of electrical charge carriers electrons.

The current is denoted with symbol uppercase letter I.

The standard unit for current is the ampere, symbolized by A.

Current is the change in charge with change in time.

Hence we can say that,

The current in a circuit can be determined as total amount of charge passes through a wire's full cross section area.

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The electrical energy used = 3.11 x 107 J; option A

The energy used is calculated using the formula below:

The total power = 3450 Watts

Total time in seconds = 2.5 × 3600 = 9000 s

Energy used = 3450 × 9000 = 3.11 x 107 J

In conclusion, electrical energy is the product of power and time.

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The mass of a body if the acceleration the body used to move is given as 5 m/s-2 will be 3 kg.

Force is defined as the push or pulls applied to the body. Sometimes it is used to change the shape, size, and direction of the body.

Force is defined as the product of mass and acceleration. Its unit is Newton.

Given data;

Force,F = 30 N

Mass,m =  kg

Acceleration,a = 5 m/s²

The force is found as;

F=ma

30 N =m kg × 5 m/s²

m=3 kg

Hence the mass of a body will be 3 kg.

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The speed or the linear velocity of the stone is 9.93 m/s; option C

The linear velocity of the stone is given by the formula below:

where w is angular velocity and r is radius.

w = θ/t

1 complete revolution = 2π radians

5 revolutions = 10π radians

w =  10π/4.4 rad/s

v = 10π/4.4 rad/s * 1.4

v = 9.93 m/s

In conclusion, the linear velocity is obtained from the angular velocity and radius of the string.

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The average speed can be calculated by dividing the total distance traveled by the total time taken.

The average speed of a vehicle can be calculated by finding the ratio of the total distance traveled and the total time taken on the journey.

Average speed = total distance covered/total time taken

Since there are markers that indicate every 100-meter journey. The total number of such marker posts encountered multiplied by 100 will give an estimate of the total distance traveled in meters.

A record of the time taken on the journey will give the total time taken.

Hence, average speed = total number of marker posts x 100/total time.

The unit will be in m/s.

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Answer: efficiency =WQH=1−TCTH

Explanation: i looked it up

The engine is rated at 400 horsepower at 6,400 rpm and 350 lb-ft of torque starting from 1,600 to 5,200 rpm.

Horsepower:

The power an engine produces is referred to as horsepower. It is determined by the amount of force required to move 550 pounds one foot in a second or 33,000 pounds one foot in a minute. The speed at which the work is completed serves as a gauge of power.

Equation to calculate horsepowe:

Simple math can be used to get horsepower: Horsepower = Torque x RPM / 5,252. To test it out for yourself, use the horsepower calculator below. Knowing a few more fundamental terminology and formulas can help you comprehend how a dynamometer determines torque and power.

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Hello!

Recall that the magnetic field produced by a solenoid with a time-varying current is given by:

[tex]B(t) = \mu_0 ni(t)[/tex]

[tex]B(t)[/tex] = time-varying magnetic field (T)

[tex]\mu_0[/tex] = Permeability of free space (4π × 10⁻⁷ Tm/A)

[tex]n[/tex] = number of turns/meter (20000)

[tex]i(t)[/tex] = time-varying current

**Since we have AC current, we can use a sinusoidal function to represent the current.

Let's now figure out the expression for the current.

The typical format of a sinusoidal function for current is:

[tex]i(t) = Asin(\omega t + \phi)[/tex]

A = amplitude (max current, 10 A)
ω = angular frequency (rad/sec)
φ = phase shift (we will assume there is not one since it is not given.)

We are also assuming we are starting from t = 0 s.

Now we need to solve for the angular frequency to complete our equation.

If the current changes direction every 0.01 seconds, that means that the PERIOD of the current is double this (aka, how long it takes for the current to repeat the same magnitude and direction).

Think about AC current like an oscillating mass on a spring. When the current changes directions, (every 0.01 sec), there is momentarily no current (temporarily no moving charge). The peak current will occur at the halfway point between each change in direction, or every 0.005 sec. Additionally, using this analogy, the mass on a spring changes direction TWICE before it returns to its original position, which is why our period here is double the time it takes for the current to switch directions.

So:
[tex]T = 2(0.01) = 0.02[/tex]

Now, we can convert from period to angular frequency.

[tex]\omega = \frac{2\pi}{T} = \frac{2\pi}{0.02} = 100\pi[/tex]

We have the current equation as:
[tex]i(t) = 10sin(100\pi t)[/tex]

So, our magnetic field produced by the solenoid will be:

[tex]B(t) = (4\pi *10^{-7})(20000)(10sin(100\pi t) )= 0.251sin(100\pi t)[/tex]

Since we have that figured out, we can use Faraday's Law to find the induced emf:
[tex]\epsilon = -N \frac{d\Phi_B}{dt}[/tex]

ε = Induced EMF (V)
N = number of loops in COIL (10 loops)

[tex]\Phi_B[/tex] = Magnetic Flux (Wb)

The area of the coil is constant so we can rewrite the equation as:
[tex]\epsilon = -N * A\frac{dB}{dt}[/tex]

Where 'A' is the cross-sectional area of the COIL.

Let's calculate that:
[tex]A = \pi (0.01^2) = 0.000314 m^2[/tex]

Now, let's calculate the induced emf. Using our equation for 'B' we got earlier:
[tex]B(t) = 0.251sin(100\pi t)\\\\\frac{dB}{dt} = (100\pi)(0.251)cos(100\pi t) = 78.957cos(100\pi t)[/tex]

Combining this into Faraday's equation:
[tex]\epsilon = -N * A\frac{dB}{dt}\\\\\epsilon = -(10)(0.000314)(78.957cos(100\pi t) = -2.48cos(100\pi t)[/tex]

The magnitude is the absolute value, so:
[tex]\epsilon = \boxed{2.48cos(100\pi t) \text{ V}}[/tex]

Answer:

See below

Explanation:

You have to heat the calorimeter to 100 C  from 20 C

  this will take   .20 kg *    390 j /kg-C   *  80 C = 6240 j

You have to heat the mass of water to boiling point (100 C ) from 20C

this will take    

    .50 kg * 4182 j/kg-C  * 80 = 167,280 j

AND you have to add enough heat to boil off  .03 kg of water:

   .03 kg * (2260000 j/kg-C )  = 67,800 j

Power = joules / sec =  (6240 + 167280 + 67800) / 274.8 = 878 watts

Your answer may differ just a bit for slightly different or rounded values of specific heat or heat of fusion for water .....

Answer:

The horizontal component of velocity (B) remains constant because no components of the external force act on this component of velocity

(the force of gravity affects the vertical component of velocity)

A hydroelectric power station turns energy from kinetic into electrical.

Thus, we can conclude that hydroelectric power station turns energy from kinetic into electrical.

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Color of third band of a coded resistor is Brown.

What is Resistance:

The color code specify the resistance value, the tolerance, and sometimes the reliability or failure rate.

How to identify resistor's color codes:

Here,

the value of resistance is 2.3x10^2 Ω

R = 23x10^1 Ω

here power of 10 is 1

so, the color of third band of a color coded resistor will be related to number 1

Hence,

color of third band of a coded resistor is Brown.

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The final velocity for object a is 5.6 m/s in the opposite direction.

From the conservation of momentum, we know that the collision between two objects will result in the conservation of initial momentum and the final momentum i.e.,

                                    Pi  =  Pf

It is given that,

                      m₁ = 1.5 kg

                       u₁ = 11.2 m/s

                       m₂= 4.5 kg

                        u₂= 0

                         v₂= 5.6 m/s

We need to find v₁.

              Using momentum conservation

               m₁ u₁ + m₂ u₂ =  m₁ v₁ + m₂ v₂

               1.5 × 11.2 + 4.5 × 0 =  1.5 × v₁ + 4.5 × 5.6

                                   16.8 + 0 =  1.5 × v₁ +  25.2

                                  -8.4/ 1.5  =  v₁

                                    v₁ = - 5.6 m/s

Here, the negative sign shows that body is moving in the opposite direction.

Hence, option (d) is correct.

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The deflection angle would have been 37.29º if the prism had been made of polystyrene plastic.

As we know that the deflection angle is an angle between the moving object from its directed course.

In the following question the deflection angle as laser enters the beam is, B = 22.6º

refractive index of glass, n1= 1.52

refractive index of polystyrene plastic, n2 = 1.59

Now when we see for the second surface then ,

B  = 45º - 22.6º

B  = 22.40º

So from Snell's law:

n1 sinθ1 = n2 sinθ2

→ sin B / sinθ = n1 / n2

sinθ = (sin 22.40º) × ( 1/ 1.59)

θ = 37.29º

Thus, the deflection angle should be 37.29º if the prism is made of polystyrene plastic.

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Answer:

bussy

Explanation:

shart

Answer:

An electrically polarized object can have zero net charge, while a charged object cannot have zero net charge.

I hope this helps :D

Answer:

v = 10m/s.

Explanation:

100 = 1/2×2×v^2

100 = 1×v^2

v^2 = √100

v=10 m/s

The centripetal acceleration of the satellite will be less than acceleration due to gravity on earth (g).

Calculation of centripetal acceleration of satellite:

Let the radius of earth be, R

Let the radius of satellite be, R'

Let the gravitational constant be, G

Let the acceleration due to gravity (earth) be, g

Let the mass of earth be M

Step 1:

We know that the orbital velocity of satellite can be given as:

v =√GM/R'     - ( 1 )

Thus, the centripetal acceleration of the satellite will be:

a_c = v²/R' = GM/R'²            - ( 2 )

The acceleration due to gravity is given as:

g = GM/R²                             - ( 3 )

Step 2:

From equation 2 and 3 we get:

a_c/g = GM/R'² ÷ GM/R²

a_c/g = R²/R'²  < 1  

Step 3:

Thus we get:    

a_c/g < 1

a_c < g

Therefore, the centripetal acceleration of the satellite is smaller than acceleration due to gravity on earth.

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You should slow your pwc to "slow, no wake speed" when within 100 feet of anchored vessels or non-motorized craft.

This is the process of operating a personal watercraft at the slowest possible speed.

This helps to maintain steerage which prevents different forms of accident or risks when in motion in the water.

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The corresponding height of the given parallelogram is 5.4 units

steps involved:

Given that the basis of the parallelogram RSTU is thought to be the line segment RU with vertices R(1, 1) and U(4, 5).

The parallelogram's top is therefore defined as the line segment ST with vertices S(7, 0) and T(10, 4).

The length of a line with endpoints at RU and ST and that is perpendicular to both RU and ST is the length that corresponds to the parallelogram's height.

Given by is the equation for the line segment RU.

Let the slope of the line perpendicular to line RU be m, then provided that two lines are perpendicular, the product of the slope of the two lines is -1.

Consequently, the equation for the line passing through point (1, 1) and perpendicular to RU is

Therefore, the corresponding height of the given parallelogram is 5.4 units

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Potential and kinetic energy both decrease with the acorn's falling potential and kinetic energy.

The acorn's potential energy is at its peak when it reaches the top of the tree, yet its kinetic energy is zero (i.e., it is not accelerating).

The height of the ball reduces along with the potential energy as the acorn tumbles down the tree, but the kinetic energy rises (energy due to motion)

The height will be 0 and the kinetic and potential energy will be zero at the ground. This demonstrates that as an item falls, both potential and kinetic energy are lost.

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The magnetic flux through one turn of the wire making the solenoid is 7.88*10^-7 T m^2.

B = unI

= 4pi*10^-7*(100/0.1)*2

= 0.00251 T

Therefore, Flux = B*Area

= 0.00251*pi*(0.01^2)

= 7.88*10^-7 T m^2

Magnetic flux is a measurement of the entire magnetic discipline which passes thru a given vicinity. It's far a useful device for helping describe the outcomes of the magnetic pressure on something occupying a given vicinity. The size of the magnetic flux is tied to the specific location chosen.

The SI unit of magnetic flux is the Weber (Wb). A flux density of 1 Wb/m2 (one Weber in keeping with rectangular meter) is one Tesla (T).

A magnetic subject describes a location in which a magnetic pressure may be felt. Magnetic flux describes how a good deal of magnetic discipline passes through a place.

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C) A current is induced in the coiled wire, which lights the light bulb

The moving magnetic field creates electricity which lights the light bulb

Hope it helps!

Answer:

C) A current is induced in the coiled wire, which lights the light bulb

Explanation:

Head restraints are energy-absorbing device that protects against such injuries.

Head restraints are a car protection characteristic, connected or included into the pinnacle of each seat to restrict the rearward motion of the grownup occupant's head, relative to the torso, in a collision to save you or mitigate whiplash or damage to the cervical vertebrae.

Powerful head restraints are designed to reduce the rearward motion of the head in a rear-end crash and reduce the probability of occupants maintaining whiplash neck injuries. Head restraints are generally known as head rests.

Make certain the top of the top restraint is at least a degree from the pinnacle of your head. The role is the pinnacle restraint so it's as near the again of your head as possible. You may need to alter the again of seat.

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Answer:

according to the Archimedes principle , the floating substance displaces some liquid, so when the ice melts ,there will be no change in the water level as the melted ice will occupy the same volume as it was occupying earlier.

Explanation: