The cannon on a battleship can fire a shell a maximum distance of 36.0 km.
(a) Calculate the initial velocity of the shell.
m/s

(b) What maximum height does it reach? (At its highest, the shell is above a substantial part of the atmosphere--but air resistance is not really negligible as assumed to make this problem easier.)
m

(c) The ocean is not flat, since the earth is curved. How many meters lower will its surface be 36.0 km from the ship along a horizontal line parallel to the surface at the ship?
mDoes your answer imply that error introduced by the assumption of a flat earth in projectile motion is significant here? (Select all that apply.)
The error is insignificant compared to the distance of travel.
The error is significant compared to the distance of travel.
The error could be significant compared to the size of a target.
The error is insignificant compared to the size of a target.

B. The meaning of 'atomos' according to Democritus in 450 BCE is indivisible.

A Greek philosopher  known as Democritus first thought of the existence of tiny particles that compose everything around us.

Democritus of Abdera, named the building blocks of matter atomos, meaning literally “indivisible.

Thus, the meaning of 'atomos' according to Democritus in 450 BCE is indivisible.

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The time taken for the bus to travel 95.1 m is 2.8 s

v² = u² + 2as

v² = 26.8² + (2 × 4.73 × 95.1)

v² = 1617.886

Take the square root of both sides

v² = √1617.886

v = 40.2 m/s

v = u + at

40.2 = 26.8 + (4.73 × t)

Collect like terms

4.73 × t = 40.2 - 26.8

4.73 × t = 13.4

Divide both side by 4.73

t = 13.4 / 4.73

t = 2.8 s

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The acceleration is  1.55 m/s^2 while is component that is parallel to the ground is 0.775  m/s^2.

The term acceleration is the rate of change of speed. Given that the distance covered is 35.0 m and the final velocity is 10.43 m/s it the follows that;

v^2 = u^2 + 2as

u = 0 because he started from rest

v^2 = 2as

a = v^2/2s

a = (10.43 m/s)^2/2 * 35.0 m

a = 1.55 m/s^2

The component of this acceleration which is parallel to the ground is;

ax = a sin θ

ax =  1.55 m/s^2 cos 60

ax = 0.775  m/s^2

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The maximum height reached by the human cannonball is 4.74 m.

The height reached is calculated as follows;

H = u²sin²θ/2g

where;

H = (15² x [sin(40)]² )/(2 x 9.8)

H = 4.74 m

Thus, the maximum height reached by the human cannonball is 4.74 m.

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The distance car moves with an average speed of 75 km/hr from town P to town Q in 2 hours is 149,760 m.

Given:
Speed = 75 km/hr

Time = 2 hr

The distance can be calculated from the product of velocity and time.

The standard unit of distance is a meter.

Convert speed and time into meters per second and seconds:

v = 75×5/18

v = 20.8 m/s

t = 3600×2

t = 7200 s

The distance is computed as:

v = d/t

d = vt

d = 20.8×7200

d = 149,760 m

Hence, the distance car moves with an average speed of 75 km/hr from town P to town Q in 2 hours is 149,760 m.

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Static friction keeps the car from skidding off the road and points toward the center of the curve. By Newton's second law, the car experiences

• net vertical force

F [normal] - F [weight] = 0

• net horizontal force

F [friction] = ma = mv²/r

where v is the tangential speed of the car.

It follows that

F [normal] = F [weight] = mg

and when static friction is maximized at the car's maximum speed,

F [friction] = µ F[normal] = 0.402 mg

Solve for v :

0.402 mg = mv²/r   ⇒   v = √(0.402 g (93.5 m)) ≈ 19.2 m/s

The upward force exerted on the board by the support is 530.8 N.

The sum of the upward forces is equal to sum of downward forces;

total downward forces = 52.8 N + 206 N + 272 N = 530.8 N

downward force = upward force = 530.8 N

Thus, the upward force exerted on the board by the support is 530.8 N.

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The depth of the well at the given air temperature is 456.3 m.

The depth of the well is calculated from the principle of echo.

v = 2d/t

2d =  vt

d = vt/2

where;

d = (338 x 2.7)/2

d = 456.3 m

Thus, the depth of the well at the given air temperature is 456.3 m.

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The upward force exerted on the board by the support is 530.8 N.

The sum of the upward forces is equal to sum of downward forces;

total downward forces = 52.8 N + 206 N + 272 N = 530.8 N

downward force = upward force = 530.8 N

Thus, the upward force exerted on the board by the support is 530.8 N.

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Due to density, the two bats have the same size, shape, and mass.

The two bats could be the same size, shape, and mass if they have the same density because density is directly proportional to mass so if the density same, the mass will also be the same.

So we can conclude that due to density, the two bats have the same size, shape, and mass.

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The concept of a black hole seem reasonable to me because of its valid and authentic evidences.

A black hole is a region in space where light is unable to escape due to strong gravitation force. The strong gravity is formed because matter has been pressed into a tiny space. This compression occurs at the end of a star's life. Some black holes are formed when a stars die.

So we can conclude that the concept of a black hole seem reasonable to me because of its valid and authentic evidences.

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The density of the mixture is determined as 1,013.75 kg/m³.

The density of the mixture is calculated as follows;

density = total mass of the mixture / total volume of the mixture

mass of the fresh water = density x volume

                                        = 1000 kg/m³ x 0.0018 m³

                                        = 1.8 kg

mass of the sea water = 1025 kg/m³ x 0.0022 m³

                                     = 2.255 kg

Total mass = 1.8 kg + 2.255 kg = 4.055 kg

Total volume = 0.0018 m³  + 0.0022 m³ = 0.004 m³

Density = 4.055 kg/0.004 m³ = 1,013.75 kg/m³

Thus, the density of the mixture is determined as 1,013.75 kg/m³.

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The magnitude of the tension in the string marked A and B is mathematically given as

Generally, the equation for is mathematically given as

The angle at A is...

[tex]tan\theta = 3/8[/tex]

When below the negative x.

B= tan\phi

[tex]tan\phi = 5/4[/tex]

When below the negative x

C=

[tex]tan \rho = 1/6[/tex]

Hence, considering the Horizontal components

74.9cos(9.46) = A*cos(20.6) + B*cos(51.3)

A = 78.9 - 0.668B

Hence, considering the Vertical components

74.9*sin(9.46) + Asin(20.6) = Bsin(51.3)

40.07 = 1.015B

B = 39.5 N

In conclusion, Sub the value of B is the equation of A

A = 78.9 - 0.668B

Sub

A = 78.9 - 0.668( 39.5 N)

A = 52.5 N

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The angular acceleration of the cylinder is mathematically given as

[tex]\alpha = 60.2175 rad/s^2[/tex]

Question parameters

Generally, the equation for Torque generated in the cylinder is  mathematically given as

[tex]\sigma[/tex] = w×r

for circular motion torque is

[tex]\sigma = × \alpha[/tex]

t[tex]=0.5 × m ×r^2 × \alpha\\\\ =0.5 × 2.15 ×0.111 ^2 × \alpha[/tex]

t = 0.0132 ×[tex]\alpha[/tex]

Therefore

0.0132 × [tex]\alpha[/tex] = w × r

[tex]\\\\\alpha =\frac{ 7.161 0.111}{(0.0132)}[/tex]

[tex]\alpha = 60.2175 rad/s^2[/tex]

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The design that would be used to make an efficient commercial vehicle chassis that has many realistic truck components is:

This refers to the main vehicle structure of a car that bears all the main stress that other components are attached to.

Hence, we can see that to make a good design for an efficient commercial vehicle chassis that has many realistic truck components, we would have to consider various factors such as handling maximum stress, maximum equilateral stress, and deflection.

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Answer:

oa

Explanation:

it may be oa is the right answer for this question

but I don't know properly

Assuming players stick together immediately after the collision, their speed will be 1.3206 m/sec, and - ve indicates their direction.

According to the law of conservation of momentum, the momentum of the body before the collision is always equal to the momentum of the body after the collision.

The given data in the problem is;

(m₁) is the mass of 1st player= 101.0 kg

(u₁) is the initial velocity of 1st player (u₁) = 4.10 m/s

(m₂) is the mass of 2nd player = 117 kg

(u₂) is the initial velocity of 2nd player= -6  m/s

(v) is the velocity after collision =.?

According to the law of conservation of momentum;

Momentum before collision =Momentum after collision

m₁u₁+m₂u₂=(m₁+m₂)V

101.0 kg × 4.10 m/sec + 117 kg × (-6 m/sec) = (101.0 kg + 117 kg) × V

V= - 1.3206 m/sec

Hence, the velocity of players just after impact, if they cling together, will be - 1.3206 m/sec, and - ve shows the direction.

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Answer:

Fruit Punch

Explanation:

A pure substance is whereby there is only one type of element or a compound in the periodic table in the substance.

Carbon: Well its just C in the periodic table, so this is definitely pure.

Water Molecule: What makes water? H2O right? Contains Hydrogen and Oxygen, and as we all know H2O is a compound, therefore this is a pure substance.

Fruit Punch: What makes fruit punch, water and fruits. Fruits may contain citric acid(a compound itself), and is mixed with water with already has a compound, so having 2 different compounds will result in a mixture and therefore it will not be pure.

The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other.

We know that graphite is composed of layers. These hexagonal layers are held together by weak Van Der Walls forces and as such are able to slide over each other. The carbon atom in each layer are held together by strong covalent bonds.

The fact that the layers of graphite are held together by only weak Van der Walls forces implies that they can slide over each other and as such make the graphite fluid.

Thus, the image that shows these layers of graphite is attached to this an answer

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Answer:it’s B

Explanation:

The answers are as follows;

a) the inductive reactance is 322 ohm

b) The maximum voltage is 387.5 V

c) The rms and maximum currents in the inductor are 1.2 A and 0.85 A.

The reactance is obtained from;

XL = 2πfL

XL = 2 * 3.14 * 57.0 * 0.900

XL = 322 ohm

The maximum voltage is obtained as;

Vo = Vrms * √2

Vo =  274 V * √2

Vo = 387.5 V

Io = Vo/XL

Io =  387.5 V/ 322 ohm

Io = 1.2 A

Irms = 274 V/322 ohm

Irms = 0.85 A

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The prompt above requires an explanatory essay. The focus of an explanatory essay is to give clarity to a concept. See the sample below.

From history, it is clear that Science builds on itself. For avoidance of doubt, this means that improvements in science are incremental with each improvement feeding off the last.

From the lesson we have examples of this phenomena such as that of Galileo. Recall that the text indicates that He improved the telescope; and while carrying out the same research that his predecessor Copernicus had done in relation to the stars and planets, Galileo used math to justify his position.

It is also on record that Johannes Kepler who lived in the same period as Galileo took interest in Astronomy. In this case, science built on itself because, Kepler's work served as the foundation for Sir Isaac Newton's work. This is also another example of how science builds on itself.

From the above textual evidence, it is given beyond reasonable double that science indeed builds on itself with the discovery of each generation serving as the foundation for the advancement of the next.

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The magnitude of the force exerted on the ship by the artillery shell will be 27× 10⁶ N.

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 = ?

Mass,m = 1350-kg

Acceleration,a = 2.00 ✕ 10⁴ m/s²

The magnitude of the force exerted on the ship by the artillery shell is found as;

F=ma

F=1350-kg × 2.00 ✕ 10⁴ m/s²

F= 10,000 N

The magnitude of the force exerted on the ship by the artillery shell will be 27× 10⁶ N.

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Answer:

(a) The rms voltage across the resistor is given by V = (2.20 102 V) sin 2ft.

V = (2.20 102 V) sin 2ft

V = (2.20 102 V) (0.707)

V = 1.56 102 V

(b) The rms current flowing through the resistor is given by I = V/R.

I = V/R

I = (1.56 102 V)/(1.90 102 Ω)

I = 8.21 A

Review procedures and confirm results to avoid possible errors.

Explanation:

Answer:

A. the center of mass

Explanation:

[tex]C_m[/tex] is usually used to designate the center of mass of an object or system of objects.

B. is incorrect because the combined mass of a system is usually denoted by ∑m.

C. is incorrect because the momentum of a system is denoted by the letter p.

Hi there!

1.

Let's use the rotational equivalent of Newton's Second Law.

[tex]\Sigma \tau = I\alpha[/tex]

τ = Torque (Nm)

I = Moment of Inertia (1/2mR² for solid cylinder)

α = Angular acceleration (rad/sec²)

The torque is equivalent to:
[tex]\tau = r \times F[/tex]

r = distance from lever arm to pivot point, aka the radius for this cylinder (0.111 m)
F = applied force (7.161 N)

We are already given various values, so let's create a working equation and solve.

[tex]rF = I\alpha \\\\\alpha = \frac{rF}{I}[/tex]
[tex]\alpha = \frac{(0.111)(7.161)}{\frac{1}{2}(2.15)(0.111^2)} = \boxed{60.013 \frac{rad}{sec^2}}[/tex]

2.

So, let's begin by doing a summation of forces acting on the block.

We have its force of gravity downward(+), and the tension from the string upward. (-), assigning signs based on the path of the falling block.

[tex]\Sigma F = F_g - T\\\\\Sigma F = m_b g - T\\\\m_b a = m_b g - T[/tex]

Solving for 'T':

[tex]T = m_b g - m_b a[/tex]

Let's now do a summation of torques on the cylinder. We only have the torque caused by the tension in the string connected to the block.

[tex]\Sigma \tau = rT\\\\I\alpha = r(T = m_b g - m_b a)[/tex]

Using the relationship between angular and translational acceleration:

[tex]a = \alpha r\\\\alpha = \frac{a}{r}[/tex]

And the equation for the moment of inertia:
[tex]I = \frac{1}{2}Mr^2[/tex]

Simplify the expression.

[tex]\frac{1}{2}Mr^2(\frac{a}{r}) = r( m_b g - m_b a)\\\\\frac{1}{2}Ma = ( m_b g - m_b a)[/tex]

Solve for 'a':
[tex]\frac{1}{2}ma + m_b a= m_b g \\\\a = \frac{m_b g}{\frac{1}{2}M + m_b} = \frac{0.730(9.81)}{\frac{1}{2}(2.15) + 0.730} = \boxed{3.97 \frac{m}{s^2}}[/tex]

3.

This is just a case of kinematics since we have a constant acceleration. To solve for this instance, however, let's use calculus.

We know that:
[tex]a(t) = 3.97[/tex]

v(t) is the integral. There is no initial velocity (block starts from rest), so:
[tex]v(t) = 3.97t + C\\C = 0 m/s \\\\v(t) = 3.97t[/tex]

Now, we can take the integral of the velocity/time equation to find the displacement between the interval.

[tex]\int\limits^{0.590}_{0.390} {3.97t} \, dt = \boxed{0.389 m}[/tex]

4.

So, let's now find the translational acceleration produced by the new cylinder. Use the kinematic equation:
[tex]\Delta x = v_0 t + \frac{1}{2}at^2[/tex]

Since the block starts from rest, we can do some simplifying and rearranging:
[tex]2\Delta x = at^2\\\\a = \frac{2\Delta x}{t^2} = \frac{2(0.450)}{0.490^2} = 3.748 \frac{m}{s}^2[/tex]

So, let's go back to our summation of torques equation. This time, however, we cannot simplify 'I'.

[tex]I(\frac{a}{r}) = r( m_b g - m_b a)[/tex]

Solving for 'I':
[tex]I = \frac{r^2( m_b g - m_b a)}{a} = \frac{(0.111^2)(7.161 - .730(3.748))}{3.748}\\\\ = \boxed{0.0145 kgm^2}[/tex]

Answer:it's 132.2m

Explanation:

Hello !

Because first recall parabolic peak height equation and

given that v=47.4m/s , h=10.5m

secondly recall parabolic total distance equation

The distance from the base of the wall that the cannonball land will be 138.7 m.

Consider that a body of mass 'm' is projected with a velocity of projection 'v' and angle of projection 'θ'. Assume that 'h' be the maximum height attained by the projectile.

2gh = v²sin²θ

This expression can be used to calculate the maximum height of the projectile.

Given, the height of the castle wall, h = 10.5 m

The velocity of the cannonball, v = 47.4m/s

The peak height equation can be used to find the angle θ:

v²sin²θ = 2gh

(47.4)² sin²θ = 2(9.81)(10.5)

Sinθ = 0.3028

θ = 17.63°

Therefore, the distance (d) from the base of the wall that the cannonball land:

d =  (47.4)² × 2 sin(17.63) / 9.81

d = 138.7m

Therefore the distance from the base of the wall that the cannonball land is 138.7m.

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The cost of gas is $1.27 per liter and the gallon of gas costs $4.80. where 1 gallon is equal to 3.78541 liters.

To convert the cost of gas from dollars per liter to dollars per gallon, The conversion factor between liters and gallons.

1 gallon is equal to 3.78541 liters (the exact conversion factor is 3.785411784).

Given the cost of gas is $1.27 per liter, let's calculate the cost per gallon:

Cost per gallon = Cost per liter × Liters per gallon

Cost per gallon = $1.27 × 3.78541

Cost per gallon = $4.80

So, a gallon of gas costs $4.80.

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Use the fundamental theorem of calculus.

[tex]f(t) = f(0) + \displaystyle \int_0^t f'(u) \, du[/tex]

In order to find velocity and position exactly, you need to know the initial velocity and position.

1) Integrate the acceleration function to get the velocity function. By the FTC,

[tex]v(t) = v(0) + \displaystyle \int_0^t a(u) \, du[/tex]

[tex]v(t) = v(0) + \displaystyle \int_0^t (3u^3+2u^2) \, du[/tex]

[tex]v(t) = \dfrac34 t^4 + \dfrac23 t^3 + v(0)[/tex]

At [tex]t=2\,\rm s[/tex], the velocity is

[tex]v(2) = \dfrac34 2^4 + \dfrac23 2^3 + v(0) = \boxed{\dfrac{52}3 + v(0)}[/tex]

2) Integrate the velocity function to the get the position function. By the FTC again,

[tex]x(t) = x(0) + \displaystyle \int_0^t v(u) \, du[/tex]

[tex]x(t) = x(0) + \displaystyle \int_0^t \left(\frac34 u^4 + \frac23 u^3 + v(0)\right) \, du[/tex]

[tex]x(t) = \displaystyle \frac3{20} t^5 + \frac16 t^4 + v(0) t + x(0)[/tex]

At [tex]t=4\,\rm s[/tex], the object's position is

[tex]x(4) = \dfrac3{20}4^5 + \dfrac16 4^4 + 4v(0) + x(0) = \dfrac{2944}{15} + 4v(0) + x(0)[/tex]

Fortunately, you don't need the initial position to find the displacement, since [tex]x(0)[/tex] cancels out in the end.

[tex]\Delta x = x(4) - x(0) = \boxed{\dfrac{2944}{15} + 4v(0)}[/tex]