a
A tennis ball is hit vertically
upward with a velocity of 30 ms-1.
It takes 3 s to reach the highest
point. Calculate the maximum
height reached by the ball. How
long it will take to return to
ground?

Answer:

the motorcycle travels 522 miles in 18 seconds Explanation: 29 x 18 is 522 I'm pretty sure that's what it was asking but I don't know

Answer:

6.86 m/s

Explanation:

The minimal velocity needed is when we have only vertical motion, then i will think in the problem only in one axis.

I suppose that the only force, in this case, is the gravitational force acting on the fish.

Then the gravitational equation of the fish will be:

a(t) = -9.8m/s^2

For the velocity equation we need to integrate over time to get:

v(t) = (-9.8m/s^2)*t + v0

Where v0 is the initial velocity of the fish and is what we want to find.

For the position equation we need to integrate over time again to get:

p(t) = (1/2)*(-9.8m/s^2)*t^2 + v0*t + p0

p0 is the initial position of the fish, and because he starts one the water, the initial position is p0 = 0 m

Then the equation is:

p(t) = (1/2)*(-9.8 m /s^2)*t^2 + v0*t

p(t) = (-4.9 m/s^2)*t^2 + v0*t

We know that the maximum height is 2.4m

The value of time at which the fish gets his maximum height is when the velocity of the fish is equal to zero, then we first need to solve:

v(t) = (-9.8m/s^2)*t + v0 = 0

      t = v0/9.8m/s^2

Now we replace this in the position equation to get the maxmimum height, which is equal to 2.4m

2.4m = p( v0/9.8m/s^2) =  (1/2)*(-9.8 m /s^2)*(v0/9.8m/s^2)^2 + v0*(v0/9.8m/s^2)

2.4m = (1/2)(-v0)^2(-9.8 m /s^2) + v0^2/(9.8m/s^2))

2.4m = (1 - 1/2)*v0^2/(9.8m/s^2)

2.4m = 0.5*v0^2/(9.8m/s^2)

2.4m/0.5 = v0^2/(9.8m/s^2)

4.8m*(9.8m/s^2) = v0^2

√(4.8m*(9.8m/s^2)) = v0 = 6.86 m/s

A boat must aim upstream at an angle of 26.3° (with respect to a line perpendicular to the coast) with respect to a line should be 1.57 m/s for a boat moving at 1.75 m/s in still water.

Perpendicular lines are two different lines that cross at a right angle of 90 degrees. Here, AB and XY connect at a 90-degree angle, making AB perpendicular to XY. The two lines do not intersect and run parallel to one another. They can't possible be compared side by side.

A form is considered perpendicular if at least two of its sides are 90 degrees from one another. Shapes with perpendicular sides include the following: Square. Rectangle.

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The velocity of the cannonball is 150 m/s,  the right option is B. 150 m/s.

The question can be solved, using Newton's second law of motion.

Note: Momentum of the cannon = momentum of the cannonball.

Make v the subject of the equation.

From the question,

Substitute these values into equation 2.

Hence, The velocity of the cannonball is 150 m/s,  the right option is B. 150 m/s.

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\( \small\bf \: let \: the \: distance \: of \: the \: man \: from \: the \: cliff \: be \: x\)

\( \small\bf \: thus \: time \: taken \: by \: sound \: to \: hit \: the \: cilff \: and \: return = \frac{2x}{v} = 1\)

\( \bf \to \: x = \frac{320}{2} m = 160m\)

\( \small \bf \: thus \: the \: distance \: between \: the \: cliffs \: = 160m \times 2 = 320m\)

Protons, neutrons, and electrons are the three main subatomic particles that make up atoms.

An oxygen atom has 8 protons, 8 electrons, and its number of neutrons may vary depending on the isotope of oxygen. The more frequently encountered isotope of oxygen is oxygen-16, with 8 neutrons.

The element with 13 protons is aluminum (Al). To find the mass number, we add the number of protons and neutrons in the nucleus. Therefore, the mass number of this aluminum isotope would be 13 + 14 = 27.

If an atom has 7 electrons, it must be nitrogen (N), which has an atomic number of 7.

Number of neutrons = Mass number - Atomic number

Thus, we obtain the number of neutrons by the equation: 14 - 7 = 7

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The speed will be 0.2 m/s and the velocity will be 0 m/s.

Speed = Total Distance / Total time

We have given total distance as ( 50 + 95 ) metres and total time as 12 minutes or we can say 720 seconds.

Speed = 145/ 720 m/s

Speed = 0.2 m/s

Velocity = Total Displacement / Total time

As the initial and final is the home, hence the net displacement is 0 in that case.

In this case also the total time we have given is 12 minutes or we can say 720 seconds.

Velocity = 0 / 720 m/s

Velocity = 0 m/s

So to conclude with we can say that the speed is 0.2 m/s and the velocity is 0 m/s.

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Answer:

1) \(T_{A} = 2\pi\cdot \sqrt{\frac{l}{g} }\), 2) \(T_{B} \approx 1.137\cdot T_{A}\), where \(T_{A} = 2\pi\cdot \sqrt{\frac{l}{g} }\).

Explanation:

1) Pendulum A is a simple pendulum, whose period (\(T_{A}\)) is determined by the following formula:

\(T_{A} = 2\pi\cdot \sqrt{\frac{l}{g} }\) (1)

Where:

\(l\) - Length of the massless bar.

\(g\) - Gravitational acceleration.

2) Pendulum B is a physical pendulum, whose period (\(T_{B}\)) is determined by the following formula:

\(T_{B} = 2\pi \cdot \sqrt{\frac{I_{O}}{m\cdot g\cdot l} }\) (2)

Where:

\(m\) - Total mass of the pendulum.

\(g\) - Gravitational acceleration.

\(l\) - Length of the uniform bar.

\(I_{O}\) - Moment of inertia of the pendulum with respect to its suspension axis.

The moment of inertia can be found by applying the formulae of the moment of inertia for a particle and the uniform bar and Steiner's Theorem:

\(I_{O} = \frac{1}{2} \cdot m\cdot l^{2}+\frac{1}{24}\cdot m\cdot l^{2} + \frac{3}{4}\cdot m\cdot l^{2}\)

\(I_{O} = \frac{31}{24}\cdot m\cdot l^{2}\) (3)

By applying (3) in (2) we get the following expression:

\(T_{B} = 2\pi \cdot \sqrt{\frac{\frac{31}{24}\cdot m \cdot l^{2} }{m\cdot g \cdot l} }\)

\(T_{B} = 2\pi \cdot \sqrt{\frac{31\cdot l}{24\cdot g} }\)

\(T_{B} = \sqrt{\frac{31}{24} } \cdot \left(2\pi \cdot \sqrt{\frac{l}{g} }\right)\)

\(T_{B} \approx 1.137\cdot T_{A}\)

1. The period of pendulum A for small oscillations is  

\(T_A=2\pi\sqrt{\dfrac{L}{g}}\)

2. The period of pendulum B for small oscillations.

\(T_B=1.137.T_A\)

Simple harmonic motion is the periodic motion or back and forth motion of any object with respect to its equilibrium or mean position. The restoring force is always acting on the object which try to bring it to the equilibrium.

1) Pendulum A is a simple pendulum, whose period () is determined by the following formula:

\(T_A=2\pi\sqrt{\dfrac{L}{g}}\)

Where:

l - Length of the massless bar.

g - Gravitational acceleration.

2) Pendulum B is a physical pendulum, whose period () is determined by the following formula:

\(T_A=2\pi\sqrt{\dfrac{I_o}{mgl}}\) .............................2

Where:

m - Total mass of the pendulum.

g - Gravitational acceleration.

l - Length of the uniform bar.

Io- Moment of inertia of the pendulum with respect to its suspension axis.

The moment of inertia can be found by applying the formulae of the moment of inertia for a particle and the uniform bar and Steiner's Theorem:

\(I_o=\dfrac{1}{2}ml^2+\dfrac{1}{24}ml^2+\dfrac{3}{4}ml^2\)

\(I_o=\dfrac{31}{24}ml^2\)..................................3

By applying (3) in (2) we get the following expression:

\(T_B=2\pi\sqrt{\dfrac{\frac{31}{24}ml^2}{mgl}\)

\(T_B=2\pi\sqrt{\dfrac{31l}{24g}}\)

\(T_B=\sqrt{\dfrac{31}{24}}. (2\pi\sqrt{\dfrac{l}{g}})\)

\(TB=1.137.T_A\)

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Answer:

Explanation:

Dipole moment of a coil carrying current i with area A

M = i A , M is magnetic moment , i is current and A is area of the coil.

A = π R²

= 3.14 x ( 3470 x 10³ )²

= 3.78 x 10¹³  m²

8.00 x 10²² = 3.78 x 10¹³ x i

current i = 8.00 x 10²²  / 3.78 x 10¹³

= 2.11 x 10⁹ A .

Answer:

The elastic potential energy stored in a spring can be calculated using the formula:

E = (1/2) kx^2

where E is the elastic potential energy, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

Plugging in the given values, we get:

E = (1/2) (80 N/m) (0.1 m)^2

E = (1/2) (80 N/m) (0.01 m^2)

E = 0.4 J

Therefore, the elastic potential energy stored in the spring when it is compressed by 0.1m is 0.4 J.

Answer:

Cytokines is the answer

Explanation:

it is another word for the chemical messanger

Answer:

In the formula, F = m×a, where a represents acceleration.

Answer:

Force=mass times acceleration

Explanation:

Answer:

9v

Explanation:

Given that the water flows at speed v in a pipe of radius r.

Let \(v_2\) is the speed of water flow where the radius of the pipe is r/3.

By using the continuity equation, the mass flow rate of water is the same at all the cross-sections of the pipe, wh have

\(\rho_1A_1_v_1 =\rho_2A_2_v_2\)

Where \(\rho_1, A_1\) and \(v_1\) are the density, area of the cross-section and speed at cross-section 1 and  \(\rho_2, A_2\) and \(v_2\) are the density, area of the cross-section and speed at cross-section 2.

As the density of the water remains constant. so \(\rho_1=\rho_2\).

\(\Rightarrow A_1_v_1 =A_2_v_2 \\\\\Rightarrow (\pi r^2)v=(\pi (r/3)^2v_2 \\\\\Rightarrow r^2v=\frac {r^2}{9}\times v_2 \\\\\Rightarrow v= \frac {v_2}{9} \\\\\Rightarrow v_2=9v.\)

Hence, the speed of the water flow where the radius is r/3 is \(9v\).

Carl Rogers, along with Abraham Maslowsignificantly contributed to the humanistic psychology movement through his development of the person-centered approach and his emphasis on the individual's subjective experience and potential for personal growth.

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Answer:

I think it's A

Explanation:

he shouldn't have changed the amount of sugar, because the whole point is to see which temperature dissolves sugar more quickly.

Kinematics is the study of the motion of a system of bodies without directly considering the forces or potential fields affecting the motion. In other words, kinematics examines how momentum and energy are shared among interacting bodies.

Answer:

Explanation:

If unknown capacitance C1, C2, C3 and C4 are connected in series to one another, their equivalent capacitance of the circuit will be expressed as shown

\(\frac{1}{C_t} = \frac{1}{C_1} +\frac{1}{C_2} +\frac{1}{C_3} +\frac{1}{C_4} \\\)

Given the capacitance's 3.0 pF, 2.0 pF, 5.0 pF and X pF connected in series to each other. If the equivalent capacitance of the circuit is 0.83 pF, then to get X, we will apply the formula above;

\(\frac{1}{0.83} = \frac{1}{3.0} +\frac{1}{2.0} +\frac{1}{5.0} +\frac{1}{C_4} \\\\\\1.205 = 0.333+0.5+0.2+\frac{1}{C_4} \\\\1.205 = 1.033 + \frac{1}{C_4} \\\\\frac{1}{C_4} = 1.205-1.033\\\\\frac{1}{C_4} = 0.172\\\\C_4 = \frac{1}{0.172}\\ \\C_4 = 5.8pF\\\\\)

C₄ ≈ 6pF

Hence the value of the X capacitor is approximately 6pF

hydroelectric dam converts the potential energy stored in a water reservoir behind a dam to mechanical energy—mechanical energy is also known as kinetic energy. ... The generator converts the turbine's mechanical energy into electricity.

Hope this helps!

Answer:

Potential energy and kinetic energy are constituents of mechanical energy.

When a turbine is switched on, it rotates with mechanical energy.

Since a motor runs the turbine, it converts this mechanical energy to electrical energy.

Answer:

Waves can transfer energy over distance without moving matter the entire distance. For example, an ocean wave can travel many kilometers without the water itself moving many kilometers. The water moves up and down—a motion known as a disturbance. It is the disturbance that travels in a wave, transferring energy.

Explanation:

The theory that has been proposed that would explain the neurology of memory are;

The neurophysiology of learning  can be described as the theory that cover the three main cognitive processes and this can be regarded as core value of the the information processing system.

It should be noted that the  information processing system usually make use of the  brains  which helps to remember information through attention, perception and all this are found in the functionality of the brain system in the human system.

Therefore, All of these are correct.

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Given,

Mass of the cannon, m₁=825 kg

Mass of the projectile, m₂=1.12 kg

The velocity of the projectile, v₂=124 m/s

According to the law of conservation of momentum, the momentum of the projectile fired should be equal to the momentum of the cannon.

i.e.,

Therefore the velocity of the cannon is given by,

On substituting the known values in the above equation,

Therefore the velocity of the cannon immediately after the projectile is shot is 0.168 m/s

Answer:

The car takes approximately 6.3 seconds to slow from 22m/s to 3m/s with a constant acceleration of -2.1m/s². This is calculated using the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.

Explanation:

Answer:

The car takes approximately 6.3 seconds to slow from 22m/s to 3m/s with a constant acceleration of -2.1m/s². This is calculated using the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time

Explanation:

Answer:

P = 23400 [kg*m/s]

Explanation:

Momentum is defined as the product of force by the time of force duration. It can be determined by means of the following equation.

\(P=F*t\)

where:

P = momentum [kg*m/s]

F = force = 2600 [N]

t = time = 9 [s]

Now replacing:

\(P=2600*9\\P=23400 [kg*m/s]\)

355.7 meter/ sec is the speed of sound in air at 108°F temperature because with the increase in temperature the speed of sound increases.

The speed of sound is directly proportional to the temperature. We know that directly proportional means when the temperature increases, the speed of sound also increases while on the other hand, when the temperature decreases, the speed of sound also decreases which shows direct relationship. That's why the speed of sound is 355.7 meter/ sec in air at 108°F temperature.

So we can conclude that 355.7 meter/ sec is the speed of sound in air at 108°F temperature because with the increase in temperature the speed of sound increase.

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Explanation:

70 degrees North of west = 110 degrees

30 degrees southof east = - 30 degrees:

Vertical components added together =

  75 (sin -30)   +    55 sin 110  =  14.18  N

Horizontal components added together =

 75 cos (-30)   + 55  cos 110    = 46.14  N

Magnitude =  sqrt ( 14.18^2 + 46.14^2 ) = 48.3   N

   direction = arctan ( 14.18 / 46.14) =  ~ 17.1 North of East

Answer:

Explanation:

F = k * q * lambda * R * π * (1 - √2/2)

Substituting the given values of q, lambda, R, and k, we get:

F = (9 x 10^9 N*m^2/C^2) * (20 x 10^-9 C) * (1 x 10^-6 C/m) * (0.1 m) * π * (1 - √2/2)

F ≈ 8.58 x 10^-4 N

Therefore, the force of interaction between the half ring and the point charge is approximately 8.58 x 10^-4 N.

The frequency of the 5 waves with a length of 4m hit the shore every 2 seconds is 2.5 Hz.

This is the number of cycles completed by a wave in one second. The s.i

unit of frequency is Hert (Hz).

From the question, to calculate the frequency of 5 waves with length of 4 m that hit the shores every 2 seconds, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The frequency of the wave is 2.5 Hz.

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