A crossbow is fired horizontally off a cliff with an initial velocity of 15 m/s. If the arrow takes 4s to hit the ground, what is the range of the projectile?

Answer:

12.65 Meters / Second (m/s)

Explanation:

the problem is really easy to solve, we begin by stating the kinetic energy formula which is:

KE = (1/2)(mass)(velocity)^2

We equate 1200 J to the formula, substitute the mass, and solve for velocity either using a CAS, app, or by hand

1200J = (0.5)(15kg)v^2

v = 12.65 m/s

Answer:

W = 6000 Joule

Explanation:

Work is defined as force times distance

W = F * d

We know that F = 15N, we just need the distance (d)

Imagine you have a square lawn with length of 10 m and width of 20m. So, we want to know the the distance you have to travel to cover every square meter of the lawn.

The width of the mower is only 50 cm = 0.5 m.

This means that you have to go back and forth 40 times to cover 20m (lawn width), with a distance of 10 m (lawn length). So,

d = 10 (meter) * 40 (times) = 400 meter

Therefore:

W = (15) * (400) = 6000 J

The area of Mrs. Turner's apartment is approximately 0.05304 square feet.

To find the area of Mrs. Turner's apartment, we need to convert the measurements from the scale drawing to the actual measurements in feet, using the given scale factor of 1 inch/18 feet.

Length of apartment in feet = 6.25 inches × (1 foot/18 inches) = 0.34722 feet

Width of apartment in feet = 2.75 inches × (1 foot/18 inches) = 0.15278 feet

Now, we can calculate the area of the apartment in square feet by multiplying the length and width:

Area of apartment in square feet = Length × Width = 0.34722 feet × 0.15278 feet = 0.05304 square feet

Therefore, the area of Mrs. Turner's apartment is approximately 0.05304 square feet.

learn more about scale factor here

https://brainly.com/question/25722260

#SPJ1

Answer:

\(T_{1}\) = 14.88 N

Explanation:

Let's begin by listing out the given variables:

M = 2.7 kg, L = 3 m, m = 1.35 kg, d = 0.6 m,

g = 9.8 m/s²

At equilibrium, the sum of all external torque acting on an object equals zero

τ(net) = 0

Taking moment about \(T_{1}\) we have:

(M + m) g * 0.5L - \(T_{2}\)(L - d) = 0

⇒ \(T_{2}\) = [(M + m) g * 0.5L] ÷ (L - d)

\(T_{2}\) = [(2.7 + 1.35) * 9.8 * 0.5(3)] ÷ (3 - 0.6)

\(T_{2}\)= 59.535 ÷ 2.4

\(T_{2}\) = 24.80625 N ≈ 24.81 N

Weight of bar(W) = M * g = 2.7 * 9.8 = 26.46 N

Weight of monkey(w) = m * g = 1.35 * 9.8 = 13.23 N

Using sum of equilibrium in the vertical direction, we have:

\(T_{1}\) + \(T_{2}\) = W + w   ------- Eqn 1

Substituting T2, W & w into the Eqn 1

\(T_{1}\) + 24.81 = 26.46 + 13.23

\(T_{1}\) = 14.88 N

The length L₂ for destructive interference is  L₂ = 22 m

A sound wave is a mechanical wave which carries sound energy from one point to another.

Since two point sources S₁ and S₂, Which are in phase and emit identical sound waves of wavelength 2.0 m: The length L₁ = 21 m. A listener stands at point P: Assume the amplitude of individual sound reaching at point P does not change, to find L₂, we need to know the path difference for destructive interference.

The path difference for destructive interference is given by ΔL = (n + 1)λ/2

where

Since we require the least intensity, we have the minimum interference. So, n = 0.

So, ΔL = (n + 1)λ/2

ΔL = (0 + 1)λ/2

L₂ - L₁ = λ/2

So, making L₂ subject of the formula, we have

L₂ = L₁ + λ/2

Given that

Substituting the values of the variables into the equation, we have that

L₂ = L₁ + λ/2

L₂ = 21 m + 2.0 m/2

L₂ = 21 m + 1 m

L₂ = 22 m

So, the length L₂ = 22 m

Learn more about destructive interference here:

https://brainly.com/question/14673752

#SPJ1

The force that the boat exerted back on the truck is 2000 N in south direction.

Newton's third law of motion states that, for every action, there is an equal and opposite reaction.

Mathematically, Newton's third law of motion can be expressed as follows;

Fa = -Fb

where;

The magnitude of both forces are equal but the direction is different.

The given parameters;

If the force exerted on the boat by the truck = 2000 N north, the reaction of the boat will 2000 N south direction.

Thus, the force that the boat exerted back on the truck is 2000 N in south direction.

Learn more about Newton's third law of motion here: https://brainly.com/question/25998091

#SPJ1

The complete question is below:

a pick up truck weighing 1200 kg is pulling a boat weighing 1500 kg by applying a force of 2000 N in the north direction. What is the force that the boat exerted on the truck?

Answer:

The speed and direction of the third fragment are 2 meters per second and 54.316º, respectively.

Explanation:

The object is not under the influence of any external force, meaning that Principle of Momentum Conservation to calculation of the velocity of the third fragment:

\((m_{1}+m_{2}+m_{3})\cdot \vec {v}_{o} = m_{1}\cdot \vec v_{1} + m_{2}\cdot \vec v_{2} + m_{3}\cdot \vec v_{3}\) (1)

Where:

\(m_{1}\), \(m_{2}\), \(m_{3}\) - Masses of the first, second and third fragments, in kilograms.

\(\vec v_{o}\) - Initial velocity of the object, in meters per second.

\(\vec v_{1}\), \(\vec v_{2}\), \(\vec v_{3}\) - Velocities of the first, second and third fragments, in meters per second.

If we know that \(m_{1} = 0.5\,kg\), \(m_{2} = 1.3\,kg\), \(m_{3} = 1.2\,kg\), \(\vec v_{o} = (0,0)\,\left[\frac{m}{s} \right]\), \(\vec v_{1} = \left(-2.8, 0\right)\,\left[\frac{m}{s} \right]\) and \(\vec v_{2} = \left(0,-1.5\right)\,\left[\frac{m}{s} \right]\), the velocity of the third fragment is:

\((-1.4,0) + (0,-1.95) + 1.2\cdot \vec v_{3} = (0,0)\)

\(1.2\cdot \vec v_{3} = (1.4,1.95)\)

\(\vec v_{3} = (1.167, 1.625)\,\left[\frac{m}{s} \right]\)

The speed of the third fragment is the magnitude of the result found above:

\(v_{3} = 2\,\frac{m}{s}\)

And the direction of the third fragment is:

\(\theta_{3} = \tan^{-1} \left(\frac{1.625}{1.167}\right)\)

\(\theta_{3} \approx 54.316^{\circ}\)

The speed and direction of the third fragment are 2 meters per second and 54.316º, respectively.

Answer:

4 photovoltaic cells are required to meet monthly energy consumption of the cabin.

Explanation:

Let suppose that PV generation system produces energy at constant energy, the number of photovoltaic system to meet energy consumption of the cabin is:

\(n = \frac{E}{\dot E \cdot t}\) (1)

Where:

\(E\) - Energy consumption of the PV system, in kilowatt-hours.

\(\dot E\) - Power generation of the PV cell, in kilowatts.

\(t\) - Working times, in hours.

If we know that \(E = 720\,kWh\), \(\dot E = 0.25\,kW\) and \(t = 720\,h\), then the number of photovoltai cells is:

\(n = \frac{E}{\dot E \cdot t}\)

\(n = 4\)

4 photovoltaic cells are required to meet monthly energy consumption of the cabin.

The impact of the imagery used in paragraph six on the meaning of "On a Mountain Trail" emphasizes the fear and uncertainty of the narrator as the pack surrounds the sleigh on the trail.

The imagery in paragraph 6 paints a vivid and powerful picture of a pack of wolves surrounding the sled. Because of the narrator's inability to count the number of wolves present, this description adds to the feeling of anxiety and uncertainty. The scene reinforces the emotional impact of the scene and helps convey the protagonist's sense of vulnerability and danger.

Therefore, the correct option is C.

Learn more about imagery, here:

https://brainly.com/question/32354003

#SPJ1

(a) The amplitude of the wave is 0.2 m.

(b) The period of the wave is  4 s.

(c) The wavelength of the wave is 100 m.

(a) The amplitude of the wave is the maximum displacement of the wave.

amplitude of the wave = 0.2 m

(b) The period of the wave is the time taken for the wave to make one complete cycle.

period of the wave = 5.5 s - 1.5 s = 4 s

(c) The wavelength of the wave is calculated as follows;

λ = v / f

where;

f = 1/t = 1 / 4s = 0.25 Hz

λ = ( 25 m/s ) / 0.25 Hz

λ = 100 m

Learn more about wavelength here: https://brainly.com/question/10728818

#SPJ1

Answer:

Heat causes the molecules to move faster, (heat energy is converted to kinetic energy ) which means that the volume of a gas increases more than the volume of a solid or liquid.

Explanation:

Answer:

Answer:

An internal-combustion engine goes through four strokes: intake, compression, combustion (power), and exhaust. As the piston moves during each stroke, it turns the crankshaft.

Answer:

The engine will not work causing no movement in the wheels .

Explanation:

Remember the four stroke combustion cycle powers the wheels and if one of these parts do not work, then the car will not move .

A velocity-time graph's area under the curve represents the distance traveled. In the first 4.8 meters of its velocity, it travels a distance of 4 seconds.

In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Instead, velocity is a vector while speed is a scalar quantity.

Individuals may mistakenly believe that average speed and average velocity are merely two different names for the same quantity, but in reality, average speed depends on distance and average velocity depends on displacement. if something is moving in a different direction.

To know more about Velocity visit:

https://brainly.com/question/17127206

#SPJ4

The observation that electromagnetic radiation with energy above a certain value can eject electrons out of a metal is a piece of evidence that they have particle-like properties.

The observation that electromagnetic radiation with energy above a certain value can eject electrons out of a metal is a piece of evidence that they have particle-like properties.

This observation that electromagnetic radiation behaves like particles is known as the photoelectric effect.

It provides evidence that electromagnetic radiation exhibits particle-like properties. When EMR with sufficient energy (above a certain threshold) interacts with a metal surface, it can cause the ejection of electrons from the metal.

This behavior indicates that EMR behaves as discrete packets of energy called photons, which transfer their energy to the electrons and cause their release. The photoelectric effect supports the particle nature of EMR and is a fundamental concept in the field of quantum mechanics.

More on electromagnetic radiation can be found here: https://brainly.com/question/29646884

#SPJ1

The kinetic energy of the book after it is slids a distance of 2 meters will be 10 Joules.

The work-energy theorem states that "the work done on an object is the change in its kinetic energy".

Hence;

Kinetic energy = work done

Note that: work-done is expressed as:

Work done = f × d

Where f is force applied and d is distance traveled.

Given that:

Force applied f = 5 newton

Distance d = 2 meters

Work done = ?

Plug these values into the above formula and solve for the workdone.

Work done = f × d

Work done = 5N × 2m

Work done = 10Nm

Work done = 10 Joules

Therefore, the kinetic energy is 10 Joules.

Option B) 10 J is the correct answer.

Learn more about work done: brainly.com/question/26115962

#SPJ1

(a) The time of motion of the stone is 4.69 seconds.

(b) The maximum distance the trebuchet can be from the castle wall to be in range is 90.44 m.

(c) The maximum height reached by the stone is 26.95 m.

The time of motion of the stone is calculated as follows;

t = 2u sinθ / g

where;

t = (2 x 30 x sin50) / (9.8)

t = 4.69 seconds

The maximum distance the trebuchet can be from the castle wall to be in range is calculated as;

R = u²sin(2θ) / g

R = (30² sin(2 x 50))/(9.8)

R = 90.44 m

The maximum height reached by the stone is calculated as follows;

H = u² sin²θ / 2g

H = (30²  x (sin 50)²) / (2 x 9.8)

H = 26.95 m

Learn more about maximum height here: https://brainly.com/question/12446886

#SPJ1

Complete Question

Complete Question is attached below

Answer:

\(q=1.558*10^{-9}c\)

Explanation:

From the question we are told that:

Side length s=1.13m

Left field strength \(E_l=784.75N/m\)

Right field strength \(E_r=776.38 N/m\)

Front field strength \(E_f=725.5 N/m\)

Back field strength \(E_b=749.54 N/m\)

Top field strength \(E_t=944.95 N/m\)

Bottom field strength \(E_{bo}=1082.58 N/m\)

Generally, the equation for  Charge flux is mathematically given by

\(\phi=EAcos\theta\)

Where

Theta for Right,Left,Front and Back are at an angle 90

\(cos 90=0\)

Therefore

\(\phi =0\) with respect to Right,Left,Front and Back

Generally, the equation for  Charge Flux is mathematically also given by

\(\phi=\frac{q}{e_o}\)

Where

\(Area =L*B\\\\A=1.13*1.13\\\\A=1.2769m^2\)

Therefore

\(Q_{net}=E_{bo}Acos\theta_{bo} +E_tAcos\theta_t\)

\(Q_{net}=1082.85*1.2769*cos0=944.95*1.2769cos (180)\)

\(Q_{net}=176N/C m^2\)

Giving

\(q=\phi*e_0\)

\(q=176N/C m^2*1.558*10^{-12}c\)

\(q=1.558*10^{-9}c\)

A source travelling in the direction of the observer causes Doppler blueshift.

When an object is moving towards us, the light from the object is known as blueshift.

The phrase refers to any relative motion, that causes a decrease in the wavelength and rise in frequency, including those that take place outside of the visible spectrum.

During the motion of the object towards us, blueshift will happen, thus shifting light to shorter wavelengths on the blue side of the spectrum.

This causes the color to shift from the red to the blue end of the spectrum in visible light.

To learn more about blueshift, click:

https://brainly.com/question/24175684

#SPJ1

Answer:

\(56.5\ \text{s}\)

\(21.13\ \text{m/s}\)

Explanation:

v = Final velocity

u = Initial velocity

a = Acceleration

t = Time

s = Displacement

Here the kinematic equations of motion are used

\(v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{25-0}{2}\\\Rightarrow t=12.5\ \text{s}\)

Time the car is at constant velocity is 39 s

Time the car is decelerating is 5 s

Total time the car is in motion is \(12.5+39+5=56.5\ \text{s}\)

Distance traveled

\(v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{25^2-0}{2\times 2}\\\Rightarrow s=156.25\ \text{m}\)

\(s=vt\\\Rightarrow s=25\times 39\\\Rightarrow s=975\ \text{m}\)

\(v=u+at\\\Rightarrow a=\dfrac{v-u}{t}\\\Rightarrow a=\dfrac{0-25}{5}\\\Rightarrow a=-5\ \text{m/s}^2\)

\(s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0-25^2}{2\times -5}\\\Rightarrow s=62.5\ \text{m}\)

The total displacement of the car is \(156.25+975+62.5=1193.75\ \text{m}\)

Average velocity is given by

\(\dfrac{\text{Total displacement}}{\text{Total time}}=\dfrac{1193.75}{56.5}=21.13\ \text{m/s}\)

The average velocity of the car is \(21.13\ \text{m/s}\).

Answer:

Gravitational

Explanation:

a. the landing ramp should be placed at 276.298 ft horizontally from the launch point.

(b) the angle of the landing ramp is 30°.

(a)

Launch speed = 55.0 mph * (1.467 ft/s)

= 80.685 ft/s

Horizontal distance = Launch speed * Time of flight

Vertical velocity = Launch speed * sin(30.0°)

Time to reach maximum height = Vertical velocity / g

Vertical distance = (1/2) *g * t²

and Time = √(2 * Vertical distance / g)

Total time of flight = 2 * Time to reach maximum height + Time for descent

Horizontal distance = Launch speed * Total time of flight

The Vertical velocity = 80.685 ft/s * sin(30.0°)

= 40.3425 ft/s

Time to reach maximum height = 40.3425 ft/s / 32.2 ft/s²

Time to reach maximum height  = 1.253 s

Time of descent = √(2 * 25.0 ft / 32.2 ft/s²)

Time of descent  = 0.913 s

Total time of flight = 2 * 1.253 s + 0.913 s

Total time of flight = 3.419 s

In conclusion, the horizontal distance = 80.685 ft/s * 3.419 s

horizontal distance = 276.298 ft

b.

the angle of the landing ramp is  30.0 be the same as the launch angle.

Learn more about horizontal distance at:

https://brainly.com/question/16411732

#SPJ1

Current cannot flow uphill in any of the listed options: a light bulb, a battery, a flowing water conduit, or a resistor. Hence option E) is the correct answer.

Current cannot flow uphill in any of the listed options: a light bulb, a battery, a flowing water conduit, or a resistor. In an electrical circuit, current is the flow of electric charge carried by electrons. Current flows in a closed loop, typically from the positive terminal of a power source (such as a battery) through the circuit components and back to the negative terminal. A light bulb, battery, flowing water conduit, and resistor all have specific roles within a circuit, but none of them allow current to flow uphill. In a circuit, current always flows from a higher electric potential to a lower electric potential. This is known as the direction of conventional current flow. In the case of flowing water, water flows downhill due to gravity, following the path of least resistance. Similarly, in an electrical circuit, current flows along the path of least resistance, from higher voltage (electric potential) to lower voltage. Therefore, option E) is the correct answer current does not flow uphill in any of the mentioned options.

For more question on Current

https://brainly.com/question/1100341

#SPJ11

Note Complete Question

Current can flow uphill in a:

A)light bulb

B)battery

C)flowing water conduit

D)resistor

E) none of the above

Answer:

5.35 rad/s

Explanation:

From the question, we are toldthat an Identical particles are placed at the 50-cm and 80-cm marks on a meter stick of negligible mass. This rigid body is then mounted so as to rotate freely about a pivot at the 0-cm mark on the meter stick.

Solving this question, the potential energy of the particles must equal to the Kinectic energy i.e

P.E=K.E

Mgh= m½Iω²-------------eqn(*)

Where M= mass of the particles

g= acceleration due to gravity= 9.81m/s^2

ω= angular speed =?

h= height of the particles in the stick on the metre stick= ( 50cm + 80cm)= (0.5m + 0.8m)= 130cm=1.3m

If we substitute the values into eqn(*) we have

m×9.81× (1.3m)= 1/2× m×[ (0.5m)² + [(0.8m)²]× ω²

m(12.74m²/s²)= 1/2× m× (0.25+0.64)× ω

m(12.74m²/s²)= 1/2× m× 0.89× ω²

We can cancel out "m"

12.74= 1/2×0.89 × ω²

12.74×2= 0.89ω²

25.48= 0.89ω²

ω²= 28.629

ω= √28.629

ω=5.35 rad/s

Hence, the angular speed of the meter stick as it swings through its lowest position is 5.35 rad/s

The physics behind the movement of electric charges between parallel plates is based on the principles of electrostatics. Electric charges are either positive or negative, and they are affected by electric fields.

Electric fields are created by a difference in electric potential, which is measured in volts. When a voltage is applied to a set of parallel plates, the charges within the plates will be affected by the electric field, and will move in response to it.

When a voltage is applied to a set of parallel plates, the positive charges in the plate connected to the positive voltage will be attracted to the negative voltage, while the negative charges in the plate connected to the negative voltage will be attracted to the positive voltage.

The movement of charges between the plates is also affected by the presence of any obstacles or resistances in the electric field, such as resistance in the wire. This can slow down the movement of charges and result in a decrease in the current flowing through the circuit.

In all, the movement of charges between electric parallel plates is the result of the electric field created by a difference in electric potential, and the movement of charges is called drift velocity. The movement is also affected by the presence of resistance.

Learn more about electric parallel plates from

https://brainly.com/question/28529259

#SPJ1

Answer:

hola bb como estas dime bb en que te ayudo

Explanation:

Answer:

1100 kg

Explanation:

acceleration:

\(a=(27-0)/4.5\)

\(a=6ms^{-2}\)

Newton's second law:

\(F=ma\)

\(6600=6m\\m=1100 kg\)