2.9030 cm has 4 significant digits.
TRUE OR FALSE

The velocity of the ball is 19.6 m/s and when the ball lands, it is moving at a speed of 77.134 m/s.

All objects with mass are subject to gravity, which is a fundamental force of nature. It is the force that pulls everything toward the core of a planet or other entity.

(a) The equation can be used to determine the velocity of a dropped ball.

v = v0 + a * t

where a is the acceleration caused by gravity (9.8 m/s2), v0 is the beginning velocity (0 in this case because the ball is dropped from rest), and t is the amount of time that has passed.

Therefore, if t = 2 seconds, the ball's velocity at that time would be:

v = 0 + 9.8 * 2 = 19.6 m/s

(b) The ball's final velocity is identical to its velocity when it lands. The following equation can be used to determine how long it takes the ball to touch the ground:

t = √(2h / a)

where a is the acceleration brought on by gravity (9.8 m/s2) and h is the height (in this case, 300 m) from which the ball is dropped.

Thus, the duration of time required for the ball to touch the ground is:

t = √(2 * 300 / 9.8) = √(600 / 9.8) = √(61.22) = 7.83 s

The formula: can be used to determine the ball's velocity when it lands.

v=v0 + a*t = 0 + 9.8 * 7.83 = 77.134 m/s

So, when the ball lands, it is moving at a speed of 77.134 m/s.

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A cell of inter resistance of 0.5 ohm is connected to coil of resistance 4 ohm and 8 ohm joined in parallel.If there is current of 2A in 8 ohm, the electromotive force (emf) of the cell is approximately 14.5 volts.

To find the emf of the cell, we can apply Ohm's Law and Kirchhoff's laws to analyze the circuit.

Given:

Resistance of the coil, R1 = 4 ohm

Resistance of the other resistor, R2 = 8 ohm

Current passing through the 8-ohm resistor, I = 2A

First, let's analyze the parallel combination of the 4-ohm and 8-ohm resistors.

The total resistance of two resistors in parallel can be calculated using the formula:

1/Rp = 1/R1 + 1/R2

Substituting the given values, we have:

1/Rp = 1/4 + 1/8

1/Rp = 2/8 + 1/8

1/Rp = 3/8

Rp = 8/3 ohm

Now, let's consider the total resistance in the circuit, which includes the internal resistance of the cell (0.5 ohm) and the parallel combination of the resistors (8/3 ohm).

R_total = R_internal + Rp

R_total = 0.5 + 8/3

R_total = 1.833 ohm

Now, we can find the emf of the cell using Ohm's Law:

emf = I * R_total

emf = 2 * 1.833

emf ≈ 3.667 volts

Therefore, the emf of the cell is approximately 3.667 volts.

However, it is worth noting that the given current of 2A passing through the 8-ohm resistor does not affect the emf calculation since the emf of the cell is independent of the current in the circuit.

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Answer:

If north is assumed to be the positive direction.

a = Δv/t = (vf - vi)/t = (20 - 50)/10 = - 3 m/s²

or

3 m/s² south

Answer:

The time taken to drive on this high way is 6.48 hours

Explanation:

Given;

average velocity, v = 24 m/s

distance of travel, d = 560 km = 560,000 m

The distance traveled is given by;

\(d = (\frac{v+u}{2} )t\\\\d =( 24 \ m/s)t\\\\t = \frac{d}{24} \\\\t = \frac{560,000}{24}\\\\t = 2333.33 \ s = 6.48 \ hrs\)

Therefore, the time taken to drive on this high way is 6.48 hours

Answer:

see explanation

Explanation:

The general formula for time-to-kill (60 / RPM) x (shots to kill an opponent -1) This measures the time from the moment you press the fire button to the moment your opponent is killed.

have a good day

Answer:

B. symbolic

Explanation:

The mental image formed in Terell's mind is a symbolic mental image.

A symbolic mental image helps to bring perception to imagery formed on the mind.

Answer:

Terell lives in Washington, D.C., where he can see the Potomac River from his bedroom window. When he sees this river, Terell thinks of swimming, boating, fun, and friends. What type of mental image is this?

symbolic

Explanation:

The electric field inside and outside the infinite conducting solid cylinder is given by \(E = \dfrac{c}{\epsilon_0}\)  and \(E = \dfrac{c\ a}{\epsilon_0\ r}\) respectively.

Inside the cylinder:

By symmetry, the electric field also has the same direction everywhere on the cylinder's lateral surface. The electric field is zero at the ends of the cylinder. By Gauss' Law, the electric flux through the cylinder's lateral surface is Φ = E * 2πrh, where E is the electric field. The electric flux through the two circular faces of the Gaussian surface is zero. Thus, the total electric flux through the entire Gaussian surface is \(\phi = \dfrac{Q_{enc}}{\epsilon_0}\).

\(E = \dfrac{c}{\epsilon_0}\)

Outside the cylinder:

The electric field is zero at the ends of the cylinder. By Gauss' Law, the electric flux through the cylinder's lateral surface is Φ = E * 2πrh, where E is the electric field. The total electric flux through the entire Gaussian surface is \(\phi = \dfrac{Q_{enc}}{\epsilon_0}\). Solving for the electric field,

\(E = \dfrac{c\ a}{\epsilon_0\ r}\)

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The value of R₂, given that the total resistance in a circuit with two parallel resistor is 2 ohms, is 3 ohms

The formula to obtain the total resistance in a parallel connection for two resistors is given as folllow:

Rₜ = (R₁ × R₂) / (R₁ + R₂)

With the above formula, we can obtain the value of R₂. Details below:

Rₜ = (R₁ × R₂) / (R₁ + R₂)

2 = (6 × R₂) / (6 + R₂)

2 = 6R₂ / (6 + R₂)

Cross multiply

2 × (6 + R₂) = 6R₂

Clear bracket

12 + 2R₂ = 6R₂

Collect like terms

12 = 6R₂ - 2R₂

12 = 4R₂

Divide both sides by 4

R₂ = 12 / 4

R₂ = 3 ohms

Thus, we can conclude that the value of R₂ is 3 ohms

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Answer:

A.

Explanation:

During the fall the day gets shorter hence less sunlight this results to leaves stopping their food making process. The chlorophyll breaks down, the green color disappears and the yellow to orange color becomes visible

Explanation:

Animal rearing is important for humans as they attain a wide range of food products having high nutrient values. They meet the commercial requirements of high demand for food such as dairy needs from cows, goats, and buffaloes.Animal husbandry helps in the proper management of animals by providing proper food, shelter and protection against diseases to domestic animals. It provides employment to a large number of farmer and thereby increases their living standards. It helps in developing high yielding breeds of animals by cross breeding

According to the question, the resulting angular speed (in rad/s) of the disk is 0.38 rad/s.

Angular speed is the rate at which an object or particle rotates or revolves around a point or an axis. It is measured in radians per second or revolutions per minute. Angular speed is an important concept in mechanics, astrophysics, and engineering.

In this case, the angular momentum of the person is 47.0 kg×2.80 m/s×1.54 m = 186 kg m²/s.

Therefore, the change in angular momentum of the disk is equal to the angular momentum of the person, which is 186 kg m²/s.

Using the conservation of angular momentum equation, we can find the angular speed of the disk by rearranging the equation to get ω = (ΔL)/I.Therefore, the angular speed of the disk is ω = 186 kg m²/s/486 kg m² = 0.38 rad/s.

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Answer:

True

Explanation:

The kinetic energy of an object is the energy that it possesses due to its movement or motion.

True, the amount of kinetic energy an object has depends on its mass and its speed.

The kinetic energy of a moving object is directly proportional to the square of its velocity and directly proportional to its mass.

ANSWER

EXPLANATION

Parameters given:

Mass of car, m = 9,000 kg

Mass of SUV, M = 12,000 kg

Initial speed of car, u = 8 m/s (taking East to be the positive direction)

Initial speed of SUV, U = - 7 m/s (taking West to be the negative direction)

Final speed of car, v = -6 m/s

To find the final momentum of the SUV, we have to apply the principle of conservation of momentum, which states that:

This implies that:

where pic = initial momentum of the car, pis = initial momentum of the SUV, pfc = final momentum of the car, pfs = final momentum of the SUV

We can rewrite the formula above as follows:

where MV represents the final momentum of the SUV.

Therefore, we have that the final momentum of the SUV is:

To find the speed of the SUV after the collision, we have to find the final speed of the SUV.

We have that from the formula for momentum:

Therefore, the final speed of the SUV is:

Since it is positive, the speed is due East.

Answer:

Explanation:

a = F/m

a = 30/5

a = 6 m/s²

Answer:

Acceleration is 6 meters per square seconds.

Explanation:

Data:

Use formula:

Replace:

Solve the division, remember remember that N / kg is equal to m/s²:

Answer:

490 meters

Explanation:

hope this helps!

Answer:

Explanation:

In this experiment, a block and tackle system was created using two broomsticks, a rope, and two helpers. The rope was tied to one broomstick and wrapped around the other, creating a simple pulley system. When the free end of the rope was pulled, the helpers resisted and the broomsticks did not move.

Next, the rope was woven back over the first broomstick, creating a double pulley. Pulling on the free end of the rope resulted in the broomsticks moving closer together. This demonstrated the mechanical advantage of the block and tackle system.

By adding more loops of rope over the broomsticks, the mechanical advantage was increased further. The force applied to the rope was spread out over a greater distance, resulting in less force required to move the broomsticks.

In summary, the block and tackle system increases mechanical advantage by spreading out the force applied over a greater distance. This is achieved through the use of pulleys and loops of rope, allowing a smaller force to move a larger load.

Answer: false

Explanation:

Answer:

False

Explanation:

Ever heard of hurricanes.

Initial acceleration is the acceleration of an object at a specific moment in time, typically at the start of a motion. It is the acceleration of an object at the beginning of its motion or when it is first subjected to a force.

Acceleration is a vector quantity that describes the rate at which an object's velocity changes with respect to time. It is the measure of how quickly the object's speed and/or direction is changing. An object can have varying accelerations depending on the forces acting on it, such as gravity or friction.The initial acceleration can be calculated using the formula a = v^2/r, where v is the initial velocity and r is the radius of circular path.

To solve this problem, use the conservation of energy and Newton's second law.

First, calculate the height of point B above point A.

Use the fact that the vertical component of the motorcycle's velocity is zero at the top of the circle, so the kinetic energy is entirely due to the horizontal component of velocity. Therefore, at point B, the kinetic energy of the motorcycle is equal to the potential energy it had at point A:

\(mgh = 1/2 mv^2\)

where m is the mass of the motorcycle, g is the acceleration due to gravity, h is the height of point B above point A, and v is the speed of the motorcycle at point B.

Cancel out the mass of the motorcycle, and use the given values to solve for h:

\(gh = 1/2 v^2 - 1/2 vA^2\)

\(h = (1/2 v^2 - 1/2 vA^2) / g\)

\(h = (1/2 (v^2 - vA^2)) / g\)

\(h = (1/2 ((0.04 s) t)^2 - 2^2) / 32.2 ft/s^2\)

\(h = (0.0008 t^2 - 4) / 32.2 ft\)

Next, use the fact that the motorcycle's acceleration is directed towards the centre of the circle, and has a magnitude of:

\(a = v^2 / r\)

where r is the radius of the circle. At point A, the velocity is purely horizontal, so the initial acceleration is:

\(aA = vA^2 / r\)

Use the fact that the acceleration is given by:

\(a = d(˙v)/dt\)

where ˙v is the rate of change of the velocity with respect to time. Integrating this equation gives:

v - vA = ∫a dt

v = vA + ∫a dt

Since the acceleration is constant, substitute the expression  derived for aA and integrate over the time it takes the motorcycle to travel from A to B. We can use the fact that the distance traveled along the circle is equal to the height difference h we calculated earlier, so the time it takes to travel from A to B is:

\(t = sqrt(2h / g)\)

\(t = sqrt((0.0008 t^2 - 4) / 16.1)\)

Squaring both sides and rearranging, we get a quadratic equation in t^2:

\(t^4 - 27.3t^2 + 674.5 = 0\)

Solving for t^2 using the quadratic formula, we get:

\(t^2 = 13.4 or t^2 = 50.3\)

Since the time cannot be negative, take the positive root:

t = 3.66 s

Substituting this value into the expression for the velocity,

\(v = 2 ft/s + (0.04 s/ft/s^2)(3.66 s)\)

\(v = 2.1464 ft/s\)

Therefore, the magnitude of the motorcycle's velocity when it reaches point B is approximately 2.15 ft/s. The initial acceleration is:

\(aA = vA^2 / r = (2 ft/s)^2 / 16 ft = 0.25 ft/s^2\)

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A motorcyclist is traveling along a vertical circular path. At point A, the motorcyclist has an initial velocity of vA = 2 ft/s and an initial position of s = 0. The motorcyclist increases their speed along the path at a rate of ˙v = (0.04s) ft/s^2, where s is in feet. Determine the magnitude of the motorcyclist's velocity when they reach point B. Also, what is the motorcyclist's initial acceleration at point A?

Answer:

e

Explanation:

Hooke's Law can be given as follows sometimes:

The restoring force of a spring is equal to the spring constant multiplied by the displacement from its normal position:

F = -kx

Where, F = Restoring force of a spring (Newtons, N)

k = Spring constant (N/m)

x = Displacement of the spring (m)

The negative sign relates to the direction of the applied force and by convention, the minus or negative sign is present in F = -kx. The restoring force F is directly proportional to the displacement (x), according to Hooke's law. When the spring is compressed, the displacement (x) is negative. It is zero when the spring is at its original length and positive when the spring is extended.

Practically, Hooke's Law is applicable only within a limited frame of reference, and through experimenting, this statement proves to be true. Because materials cannot be compressed beyond a certain size or expanded beyond a certain size without some permanent deformation or change of their original state.

The law only applies under some conditions such as a limited amount of force or deformation. Factually, many materials will noticeably deviate from Hooke's law even before those elastic limits are reached.

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It would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

1. The decay rate of a radioactive isotope is proportional to the number of radioactive atoms present in the sample at any given time.

2. The decay rate can be expressed as a function of time using the formula: R(t) = R₀ * \(e^{(-\lambda t\)), where R(t) is the decay rate at time t, R₀ is the initial decay rate, λ is the decay constant, and e is the base of the natural logarithm.

3. The half-life of a radioactive isotope is the time it takes for half of the radioactive atoms in a sample to decay. In this case, the half-life is given as 210 days.

4. Using the half-life, we can find the decay constant (λ) using the formula: λ = ln(2) / T₁/₂, where ln(2) is the natural logarithm of 2 and T₁/₂ is the half-life.

5. Substituting the given half-life into the formula, we have: λ = ln(2) / 210.

6. Now, we need to find the time it takes for the decay rate to fall to 0.58 of its initial rate. Let's call this time "t".

7. Using the formula for the decay rate, we can write: 0.58 * R₀ = R₀ * e^(-λt).

8. Simplifying the equation, we get: 0.58 = \(e^{(-\lambda t\)).

9. Taking the natural logarithm of both sides, we have: ln(0.58) = -λt.

10. Substituting the value of λ from step 5, we get: ln(0.58) = -(ln(2) / 210) * t.

11. Solving for t, we have: t = (ln(0.58) * 210) / ln(2).

12. Evaluating the expression, we find: t ≈ 546.

13. Therefore, it would take approximately 546 days for the decay rate of the sample of this radioactive isotope to fall to 0.58 of its initial rate.

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The wavelength of light that should be used to obtain fringes that are 0.0045 m wide after reducing the distance between the screen and the slit by half is 2.25 * 10^7 Å.

Huygens's Principle states that every point on a wavefront can be considered as a source of secondary spherical wavelets that spread out in all directions with the same speed as the original wave. The new wavefront is formed by the envelope of these secondary wavelets at a later time.

Now, let's consider a Young's double-slit experiment. In this experiment, when light passes through two narrow slits, it creates an interference pattern on a screen behind the slits. The fringe width is the distance between two consecutive bright or dark fringes in the pattern.

Given that the fringe width obtained is 0.6 cm and the wavelength of light used is 4500 Å (Angstroms), we can calculate the wavelength of light required to obtain fringes that are 0.0045 m wide.

We can use the formula for fringe width in Young's double-slit experiment:

w = (λ * D) / d

Where:

w is the fringe width,

λ is the wavelength of light,

D is the distance between the screen and the double slits, and

d is the distance between the two slits.

Let's calculate the value of D/d using the given information:

D/d = w / λ

= 0.006 m / 4500 Å (1 m = 10^10 Å)

= 0.006 * 10^10 / 4500 m^-1

Now, if the distance between the screen and the slit is reduced by half, the new value of D/d would be:

(D'/d) = (0.006/2) * 10^10 / 4500 m^-1

Now, we can rearrange the equation to solve for the new wavelength (λ'):

(λ' * D') / d = (D/d)

λ' = (D/d) * d / D

= [(0.006/2) * 10^10 / 4500] * (4500 / 0.006) Å

= 0.0045 m * 10^10 / 2 Å

= \(0.00225 * 10^{10\) Å

=\(2.25 * 10^7\)Å

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Answer:

An intermediate swimmer would probably take about four to five minutes, while a trained swimmer could take less than three. The world record is 1:42:00, held by Paul Biedermann. If you are a good swimmer you would swim it easily in 3 and a half minutes.

Explanation:

\(\\ \sf\longmapsto Speed=\dfrac{Distance}{Time}\)

\(\\ \sf\longmapsto Time=\dfrac{Distance}{Speed}\)

\(\\ \sf\longmapsto Time=\dfrac{200}{4}\)

\(\\ \sf\longmapsto Time=50s\)

\(\\ \sf\longmapsto (101010)_2\)

\(\\ \sf\longmapsto 0\times 2^0+1\times 2^1+0\times 2^2+1\times 2^3+0\times 2^4+1\times 2^5\)

\(\\ \sf\longmapsto 2+8+32\)

\(\\ \sf\longmapsto (42)_{10}\)

Answer:

Let's represent the magnitude of both vectors A and B using the variable "m".

According to the problem statement, we have:

|A| = |B| = m

|A+B| = 3|A-B|

Squaring both sides, we get:

|A+B|^2 = 9|A-B|^2

Expanding the left-hand side using the dot product formula, we have:

(A+B)·(A+B) = A·A + 2A·B + B·B

Similarly, expanding the right-hand side, we have:

9(A-B)·(A-B) = 9A·A - 18A·B + 9B·B

Substituting the given magnitudes, we have:

(A+B)·(A+B) = 2m^2 + 2(A·B)

9(A-B)·(A-B) = 18m^2 - 18(A·B)

Substituting these expressions back into the original equation, we get:

2m^2 + 2(A·B) = 9(18m^2 - 18(A·B))

Simplifying and rearranging, we get:

20(A·B) = 323m^2

Dividing by |A|·|B| = m^2, we have:

20(cosθ) = 323

where θ is the angle between vectors A and B. Solving for θ, we get:

θ = cos⁻¹(323/20)/π * 180

θ ≈ 83.4 degrees

The nature of the image formed by the convex lens is virtual, the position of the image is 30 cm away from the lens on the same side as the object, and the size of the image is twice the size of the object. The magnification is 2, meaning the image is magnified.

Given:

Object height (h) = 5 cm

Focal length of the convex lens (f) = 10 cm

Object distance (u) = 15 cm (positive since it's on the same side as the incident light)

To determine the nature, position, and size of the image, we can use the lens formula:

1/f = 1/v - 1/u

Substituting the given values:

1/10 = 1/v - 1/15

To simplify the equation, we find the common denominator:

3v - 2v = 2v/3

Simplifying further:

v = 30 cm

The image distance (v) is 30 cm. Since the image distance is positive, the image is formed on the opposite side of the lens from the object.

To find the magnification (M), we use the formula:

M = -v/u

Substituting the values:

M = -30 / 15 = -2

The magnification is -2, indicating that the image is inverted and twice the size of the object.

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