A ball thrown horizontally at 22.2 m/s from the roof of a building lands 36.0 m from the base of the building. how high is the building?

Final answer:

The question deals with the heights of volcanic lava ejections on moons within our solar system under varying gravitational conditions, highlighting Io, a moon of Jupiter. It emphasizes physics concepts like kinematics and gravitational force, and underlines the contribution of space exploration to our understanding of celestial phenomena.

Explanation:

The question explores the phenomenon of volcanic eruptions on moons in our solar system, focusing on Io, one of Jupiter's moons, and another hypothetical moon. Specifically, it mentions volcanoes ejecting lava to great heights under different gravitational conditions. The question implicitly asks for an analysis or comparison based on the given data, such as the maximum height of lava ejection and the acceleration due to gravity on another moon.

The subject matter delves into the principles of kinematics and gravitational force, which are fundamental concepts in physics. It exemplifies how extraterrestrial volcanism can offer insights into the geological and physical dynamics of celestial bodies other than Earth. Furthermore, the mention of Galileo and Voyager spacecrafts underlines the importance of space exploration in understanding these phenomena.

The length of a tropical year is approximately 365.242199 days, or approximately 31556926 seconds. Therefore, the number of seconds in two and a half tropical years is approximately 78892315 seconds.

The tropical year is based on the time it takes the Earth to revolve around the sun, and is the basis of our calendar. This time period lasts approximately 365.242199 days. To find the number of seconds in a tropical year, we need to first convert this period into hours, minutes, and then seconds. There are 24 hours in a day, 60 minutes in an hour, and 60 seconds in a minute. Here's the calculation:

So, one tropical year is approximately 31556926 seconds.

To find out the number of seconds in two and a half tropical years, we simply multiply this number by 2.5:

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If the mass of the crate is doubled but the initial velocity is not changed, the crate slides distance d before stopping.

[tex]\texttt{ }[/tex]

Let's recall the formula of Kinetic Energy as follows:

[tex]\large {\boxed {E_k = \frac{1}{2}mv^2 }[/tex]

Ek = Kinetic Energy ( Newton )

m = Object's Mass ( kg )

v = Speed of Object ( m/s )

Let us now tackle the problem !

[tex]\texttt{ }[/tex]

Given:

initial height = h₁ = 26 m

final height = h₂ = 16 m

initial speed = v₁ = 0 m/s

coefficient of friction = μ

gravitational acceleration = g

distance = d

Asked:

final speed = v₂ = ?

Solution:

We will use Work and Energy formula to solve this problem as follows:

[tex]W = \Delta Ek[/tex]

[tex]-f d = Ek_{final} - Ek_{initial}[/tex]

[tex]-\mu N d = \frac{1}{2}m (v_f)^2 - \frac{1}{2} m (v_i)^2[/tex]

[tex]-\mu mg d = \frac{1}{2}m (v_f)^2 - \frac{1}{2} m (v_i)^2[/tex]

[tex]-\mu mg d = \frac{1}{2}m (0)^2 - \frac{1}{2} m (v_i)^2[/tex]

[tex]-\mu mg d = \frac{1}{2} m (v_i)^2[/tex]

[tex]\mu g d = \frac{1}{2} (v_i)^2[/tex]

[tex]d = \frac{1}{2} (v_i)^2 \div ( \mu g )[/tex]

[tex]\boxed {d = \frac { (v_i)^2 } { 2 \mu g } }[/tex]

[tex]\texttt{ }[/tex]

From information above we can conclude that the distance is independent to the mass of the crate.

If the mass of the crate is doubled but the initial velocity is not changed, the crate slides the same distance d before stopping.

[tex]\texttt{ }[/tex]

[tex]\texttt{ }[/tex]

Grade: High School

Subject: Physics

Chapter: Dynamics

If the mass of the crate is doubled while maintaining the same initial velocity, the stopping distance will be halved. This is due to the doubled frictional force from the increased mass. Therefore, the crate will slide a distance of d/2 before coming to a stop.

Thus, the crate will slide half the distance before stopping if the mass is doubled but the initial velocity is unchanged.

Alice and Tom reach the lake simultaneously due to gravity's independence from their initial horizontal velocities. The correct answer is (E).

Let us consider the concept of horizontal motion and vertical motion of a projectile (in this case, Alice and Tom) are independent of each other when there is no air resistance.

This means that the horizontal velocity does not affect the vertical motion.

Both Alice and Tom are subject to the same gravitational acceleration, and since they are both falling vertically, they will reach the surface of the lake at the same time.

So, the correct answer is (E). Alice and Tom will reach the surface of the lake at the same time.

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Alice and tom dive from an overhang into the lake below. tom simply drops straight down from the edge, but alice takes a running start and jumps with an initial horizontal velocity of 25 m/s. neither person experiences any significant air resistance. compare the time it takes each of them to reach the lake below.

(A) alice and tom dive from an overhang into the lake below.

(B) tom simply drops straight down from the edge, but alice takes a running start and jumps with an initial horizontal velocity of 25 m/s.

(c) neither person experiences any significant air resistance. compare the time it takes each of them to reach the lake below. tom reaches the surface of the lake first.

(D) alice reaches the surface of the lake first.
(E) alice and tom will reach the surface of the lake at the same time.

Both Alice and Tom will reach the surface of the lake at the same time because their times to hit the water depend only on the vertical distance and gravitational acceleration.

Alice and Tom both dive from the same overhang into a lake below.

Both Alice and Tom experience the same vertical acceleration and fall the same vertical distance, hence, they will both reach the surface of the lake at the same time.

To find the magnitudes of vectors a and b, we need to resolve them into their x and y-components and equate them to zero to form two equations. Solving these equations will give us the magnitudes of a and b.

To find the magnitudes of vectors a and b, we need to analyze the given vector sum equation a + b + c = 0. Since vector c is in the negative y-axis direction, it can be written as c = 0î - 24.6ĵ m. According to the vector sum equation, the x-components and y-components of the vectors should cancel out each other. Using trigonometric identities, we can resolve vectors a and b into their x and y-components:

a = (ax)î + (ay)ĵ

b = (bx)î + (by)ĵ

After resolving the vectors, we equate their x-components and y-components to zero to form two separate equations. Solving these equations will give us the magnitudes of vectors a and b.

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Each leg of the stool decreases in length by approximately 1.40 × 10⁻⁴% when the 70 kg man sits on it.

Calculate the force exerted on each leg:

Given: mass (m) = 70 kg, acceleration due to gravity (g) = 9.8 m/s²

Force (F) = mass × acceleration = 70 kg × 9.8 m/s² = 686 N

Determine the original length of the legs:

Let's assume the height of the stool is 1 meter (100 cm).

Calculate the cross-sectional area of each leg:

Given the diameter of each leg is 2.5 cm, the radius (r) is 1.25 cm or 0.0125 m.

Area (A) = π × r²

Area ≈ 3.14 × (0.0125 m)² ≈ 4.91 × 10⁻⁴ m²

Determine the modulus of elasticity of Douglas fir:

Let's assume E = 10 × 10⁹ N/m².

Calculate the change in length for each leg:

Using the formula for axial deformation:

Change in length (ΔL) = (Force × Length) / (Area × Modulus of Elasticity)

ΔL = (686 N × 1 m) / (4.91 × 10⁻⁴ m² × 10 × 10⁹ N/m²)

ΔL ≈ 1.40 × 10⁻⁶ m

Calculate the percentage decrease in length:

Percentage decrease = (Change in length / Original length) × 100%

Percentage decrease = (1.40 × 10⁻⁶ m / 1 m) × 100%

Percentage decrease ≈ 1.40 × 10⁻⁴ %

So, each leg of the stool decreases in length by approximately 1.40 × 10⁻⁴% when the 70 kg man sits on it.

The question probable may be:

A three-legged wooden bar stool made out of solid Douglas firhas legs that are 2.5 cm in diameter.

When a 70 kg man sits on thestool, by what percent does the length of the legs decrease?Assume, for simplicity, that the stool's legs are vertical and thateach bears the same load.

Answer:

Initial speed, u = 2.03 m/s

Explanation:

Flea jumps to a height of, h = 21.1 cm = 0.211 m

As it leaves the ground, its final speed, v = 0

Acceleration, a = -g

Let u is the initial speed of the flea. It can be calculated as :

[tex]v^2-u^2=2as[/tex]

[tex]-u^2=2\times (-9.8)\times 0.211[/tex]

u = 2.03 m/s

So, the initial speed of the flea as it leaves the ground is 2.03 m/s. Hence, this is the required solution.

Answer:

Part a)

y = 30.625 m

Part b)

v = 24.5 m/s

Explanation:

Part a)

As we know that brick will hit the floor after t = 2.50 s

so here we will have

[tex]y = v_i t + \frac{1}{2}at^2[/tex]

[tex]y = 0 + \frac{1}{2}(9.8)(2.50^2)[/tex]

[tex]y = 30.625 m[/tex]

Part b)

velocity of the brick just before it will strike the ground is given as

[tex]v_f = v_i + at[/tex]

[tex]v_f = 0 + (9.8)(2.5)[/tex]

[tex]v_f = 24.5 m/s[/tex]

Part c)

Answer: B. standard deviation

Explanation:

In statistics , Standard deviation is a term which is used to to represent the measure of dispersion of data from the mean-value.

It is used to determine how closely the data values are with the mean of the entire data.

It is the average distance from each data value to the mean.

Hence, the average distance between the variable scores and the mean in a set of data is the standard deviation.

The resultant vector, is the vector that adds the components x and y separately.

Since the two x components are 0.00 m/s and 1.00 m/s, the resultant x component will be:

The simultaneous vector of velocity in the form of components x and y is

1, -1 m / s

Vectors are quantities that have magnitude and direction

Vector can be symbolized in the form of directed line segments

One of the presentations of vector shapes is in geometric conditions where the vector components are expressed in the form of x and y coordinates which can be described in matrix form

The position vector of a vector starts from the starting point to the endpoint

Addition of two vectors is the addition of component x and component y

A (x1, y1) and B (x2, y2)

A + B = (x1 + x2, y1 + y2)

There is additional information on the problem:

a swimmer moves to the right with a speed of 1 m / s while the current from the river with the same speed down by 1 m / s (picture attached)

so the vector component position based on components x and y becomes:

swimmer (p): (1,0)

river current (s): (0, -1)

So if the two vectors are added it will become:

v = p + s

v = (1 + 0, 0-1)

v = (1, -1) m / s

identify the components of a vector

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Michael Jordan's takeoff speed for his 47.2-inch vertical leap would be approximately 4.85 m/s, calculated using the kinematic equation for vertical motion.

To find Michael Jordan's takeoff speed, we can use the kinematic equation for vertical motion without air resistance: vf^2 = vi^2 + 2 * a * d, where vf is the final velocity (0 m/s at the peak of the jump), vi is the initial velocity (takeoff speed we want to find), a is the acceleration due to gravity (-9.81 m/s^2), and d is the vertical leap distance.

First, we convert the vertical leap from inches to meters: 47.2 inches = 1.2 meters (approximately).

Now, we can set vf to 0 m/s and solve for vi:

0 = vi^2 + 2 * (-9.81) * 1.2

vi^2 = 2 * 9.81 * 1.2

vi = sqrt(2 * 9.81 * 1.2)

vi ≈ 4.85 m/s (rounded to two decimal places)

Therefore, Michael Jordan's takeoff speed would be approximately 4.85 m/s.

Final answer:

To calculate the electric field magnitude at a distance from a charged rod, determine the charge per unit length and use the electric field formula.

Explanation:

Electric Field and Charged Rod:

To find the magnitude of the electric field at a distance from a charged rod, you can use the formula for the electric field of a long, charged rod. Given the total charge on the rod and its length, you can calculate the charge per unit length. Then, apply the formula to find the electric field at the specified location.

Let the rod be on the x-axes with endpoints -L/2 and L/2 and uniform charge density lambda (2.6nC/0.4m = 7.25 nC/m).

The point then lies on the y-axes at d = 0.03 m.

from symmetry, the field at that point will be ascending along the y-axes.

A charge element at position x on the rod has distance sqrt(x^2 + d^2) to the point.

Also, from the geometry, the component in the y-direction is d/sqrt(x^2+d^2) times the field strength.

All in all, the infinitesimal field strength from the charge between x and x+dx is:

dE = k lambda dx * 1/(x^2+d^2) * d/sqrt(x^2+d^2)

Therefore, upon integration,

E = k lambda d INTEGRAL{dx / (x^2 + d^2)^(3/2) } where x goes from -L/2 to L/2.

This gives:

E = k lambda L / (d sqrt((L/2)^2 + d^2) )

But lambda L = Q, the total charge on the rod, so

E = k Q / ( d * sqrt((L/2)^2 + d^2) )

The percent accuracy is 10⁻⁵%. It is determined by the formula of percent accuracy.

Given information:

Distance of satellite = 20,000km

= 2 x 10⁷ m

Uncertainty = 2 meter

Uncertainty refers to a lack of exactness or precision in measurement, calculation, or prediction. It represents the degree of doubt or error associated with a particular value or result. Uncertainty is an essential concept in various fields, including science, engineering, statistics, and decision-making.

The formula to determine percent accuracy is:

[tex]\rm Percent \ accuracy= \frac{Uncertainty}{Measured d\ distance} \times 100[/tex]

Substituting the values in the formula:

[tex]\rm Percent \ accuracy = \frac{2}{2\times 10^7}\times 100 \\\rm Percent \ accuracy = \frac{1}{10^5} \\[/tex]

Simplifying:

Percent accuracy = 10⁻⁵%.

Therefore, the percent accuracy is 10⁻⁵%.

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1. What is the weight of this objects?

Weight is simply the product of mass and gravitational acceleration. Therefore the weight is:

w = 20 kg * 9.81 m/s^2

w = 196.2 kg m/s^2 = 196.2 N

2. After 5 seconds, how has the object fallen and what is its speed at this instant?

We can use the formula:

y = v0 t  + 0.5 g t^2

v = v0 + g t

where v0 = 0 since the object starts from rest, y is the distance it fell, t is time

y = 0 + 0.5 * 9.81 * 5^2 = 122.625 m

v = 0 + 9.81 * 5 = 49.05 m/s

In order to maintain equilibrium and have a downslope acceleration of 0.64 m/s² with a 2.3 kg mass, the right-hand mass should be approximately 0.15 kg.

In physics, the question is referring to the concept of equilibrium through the force of gravity. When a downtrend pushes left-hand mass with a certain acceleration, it implies that any other force (potentially from another mass on the opposite direction) counteracts. This counteraction or the right-hand mass is what we are now to calculate.

Assuming there is no friction, the force acting on the left-hand mass (F1) can be calculated using Newton's second law of motion, F = ma where m is the mass and a is the acceleration, yielding F1 = 2.3 kg * 0.64 m/s² = 1.472 N

For equilibrium to be maintained, the force due to the right-hand mass (F2) must equal F1. Therefore, if g is the acceleration due to gravity (9.81 m/s²), the right-hand mass (m2) can be found using the formula m2 = F1 / g, simplifying to m2 = 1.472 N / 9.81 m/s² = 0.15 kg.

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