The fire hose, shooting water at 6.5 m/s, should be angled at [tex]\(\frac{1}{2} \sin^{-1}\left(\frac{gR}{v^2}\right)\)[/tex] to achieve a 2.0 m range. Two angles exist due to the symmetrical nature of projectile motion.
To find the angles at which the water from the fire hose lands 2.0 m away, we can use the projectile motion equations. The horizontal distance (range) can be calculated using the formula:
[tex]\[ R = \frac{v^2 \sin(2\theta)}{g} \][/tex]
where:
R is the range (2.0 m),
v is the initial velocity of the water (6.5 m/s),
[tex]\( \theta \)[/tex] is the angle of projection,
g is the acceleration due to gravity (approximately 9.8 m/s²).
Rearranging the equation to solve for [tex]\( \theta \)[/tex], we get:
[tex]\[ \theta = \frac{1}{2} \sin^{-1}\left(\frac{gR}{v^2}\right) \][/tex]
Plugging in the given values, we find two possible angles: one for the first quadrant and another for the second quadrant. This is because the sine function has the same value in the first and second quadrants. Therefore, there are two solutions for [tex]\( \theta \)[/tex].
It's important to note that for a given range, there are two launch angles that result in the same range due to the symmetrical nature of the projectile motion. These angles are complementary, meaning their sum is 90 degrees. Therefore, two possible angles will yield the water landing 2.0 m away.
Answer the following question about "The Deadliest Tsunami in History."
Survivors of the Tsunami recognized that a receding ocean
a. Was a sign of danger
b. Left pollution on shore
c. Left boats and fish stranded on shore
d. Signals a coming earthquake
The correct answer is - a. was a sign of danger.
Once the people saw that the ocean waters are receding and were living vast space without water behind them, they knew that something big and very dangerous will happen. And in fact it did. The water that was sucked in in the place were there was a crack on the ocean floor, got shot back under big pressure and it had very big speed, as well as having waves that were destroying anything on their way.
Answer:
Option (A)
Explanation:
Tsunamis are the series of large waves that are generated in the large water bodies such as seas and oceans, due to an earthquake, underwater explosion or landslide. These waves can rise up to a height of about hundreds of meters.
A receding ocean is a sign of danger that signifies that a tsunami is approaching. During this time the water level drops down unusually along the coastline. It is a kind of warning that is given to the people living in the coastal areas to evacuate it as soon as possible in order to save their lives.
Thus, the correct answer is option (A).
A compressed spring has 16.2 J of elastic potential energy when it is compressed 0.30 m. What is the spring constant of the spring?
Answer:
360
Explanation:
just took the test
Final answer:
To find the spring constant, use the formula for elastic potential energy,[tex]U = 1/2 k x^2[/tex]. Given that U = 16.2 J and x = 0.30 m, the spring constant is calculated to be 360 N/m.
Explanation:
The spring constant, denoted by k, is a measure of the stiffness of a spring. It represents the force required to stretch or compress a spring by a certain amount.
The question asks about finding the spring constant from the given elastic potential energy and displacement.
The formula for elastic potential energy stored in a spring is [tex]U = 1/2 k x^2[/tex], where U is the elastic potential energy, k is the spring constant, and x is the displacement from the equilibrium position. Using this formula and the given values, we can solve for k as follows: [tex]16.2 J = 1/2 k (0.30 m)^2[/tex]. After calculating, we find the spring constant is 360 N/m.
the pitch of a sound us most closely related to the
Which of the following statements is true about the movement of sound waves?
A. they can only travel through a vacuum
B. they can travel through air only
C. they can only travel through a medium
D. they travel fastest in gaseous mediums
Answer: The correct option is C.
Explanation:
Longitudinal wave is a wave in which the particles vibrates parallel to the direction of the energy transportation of the wave .
For example, sound wave.
Sound wave consists of rarefaction and compression. In rarefaction, the density of the particles is more in comparison to compression.
Sound wave needs a medium for its propagation. It can travel in solid, liquid and gas. It cannot travel in vacuum.
Therefore, the true statement about the movement of sound waves is only (C) option.
A 40.0 kg crate is being lowered by means of a rope. Its downward acceleration is 3.80 m/s2. What is the force exerted by the rope on the crate? A 40.0 kg crate is being lowered by means of a rope. Its downward acceleration is 3.80 m/s2. What is the force exerted by the rope on the crate?
Final answer:
The force exerted by the rope on the crate is 152.0 N.
Explanation:
To calculate the force exerted by the rope on the crate, we can use Newton's second law of motion, which states that force is equal to mass times acceleration. In this case, the mass of the crate is 40.0 kg and the acceleration is 3.80 m/s². Therefore, the force exerted by the rope on the crate can be calculated as:
Force = mass * acceleration
Force = 40.0 kg * 3.80 m/s²
Force = 152.0 N
Therefore, the force exerted by the rope on the crate is 152.0 N.
This law states that a planet's elliptical orbit around the Sun sweeps equal amounts of area in an equal amount of time. This means that each planet travels faster near the Sun and slower farther from it.
A. law of ellipses
B. law of inertia
C. equal areas law
D. harmonic law
The law is C.) Equal areas law
Suppose that two objects attract each other with a gravitational force of 16 units. If the distance between the two objects is doubled, what is the new force if attraction between the two objects?
Answer:
4
Explanation:
Galileo discovered that the orbits in which planets move around the Sun are elliptical.
True or False
Galileo discovered that the orbits in which planets move around the Sun are elliptical.
false
Answer: False
Explanation:
Galileo proved the heliocentric model by studying the position of Venus. He believed the sun to be center and all other bodies revolved around it in circular orbits which was disproved by Kepler. Kepler developed laws of planetary motion. One of which states that planets revolve around Sun in elliptical orbits with Sun at one of its foci. Thus, the given statement is false.
What increases as sound waves increase in frequency?
pitch
amplitude
decibels
loudness
Answer: pitch
Explanation:
Pitch is the perception of the frequency of a sound: this means that pitch is directly proportional to the frequency of the sound.
Therefore, if the frequency of the sound wave increases, the pitch increases as well.
1. With manual transmission, use your right foot for the brake and accelerator and left foot for the clutch. true or false
Describe several uses of plastic, and explain why plastic is a good choice for these products
The refractive index of water is greater than that of air but is less than that of glass or a diamond. under which condition can there be total internal reflection in water?
To ensure 100% internal reflection in water, the light must first pass through glass or a diamond before entering the water.
What is an index of refraction?The refractive index of a substance also known as the refraction index or index of refraction is a dimensionless quantity that specifies how quickly light passes through it in optics.
The speed at which light waves travel changes as the medium changes. The absolute refractive index changes.
Angle of incidence must be larger than critical angle for entire internal reflection.
Total internal reflection occurs in water when the refractive index on the other side of the water is lower and the angle of incidence is larger than the critical angle.
So there must be oxygen on the other side of the river. Light must go from a medium object of greater density to a medium object of lower density for total internal reflection to occur.
To ensure 100% internal reflection in water, the light must first pass through glass or a diamond before entering the water.
In the water, the angle of incidence is 50 degrees. It experiences entire internal reflection because the angle of incidence is larger than the air-water critical angle of roughly 48°.
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A 65kg person throw a 0.045kg snowball forward with a ground speed of 30m/s. A second person, with a mass of 60kg, catches the snowball. Both people on the skate. the first person is initially moving forward with speed of 2.5m/s, and the second person is initially at rest. what are the volocities of the two people after the snowball is exchanged? disregard friction between the skates and the ice
Particle A and particle B are held together with a compressed spring between them. When they are released, the spring pushes them apart, and they then fly off in opposite directions, free of the spring. The mass of A is 2.00 times the mass of B, and the energy stored in the spring was 68 J. Assume that the spring has negligible mass and that all its stored energy is transferred to the particles. Once that transfer is complete, what are the kinetic energies of each particle?
Which statement correctly describes the relationship between current, voltage, and resistance? If we
A: decrease the resistance, and do not change the voltage, the current will decrease.
B: decrease the voltage, and do not change the resistance, the current will also decrease.
C: increase the resistance, and do not change the current, the voltage will remain the same.
D: increase the current, and increase the resistance, the voltage will decrease.
Answer: Option (b) is the correct answer.
Explanation:
According to ohm's law, the relationship between voltage, resistance, and current is that current passing through a conductor is directly proportional to the voltage over resistance.
Mathematically, I = [tex]\frac{V}{R}[/tex]
From this relationship we can see that when we decrease the voltage, and do not change the resistance, the current will also decrease. As current is directly proportional to voltage and inversely proportional to resistance.
What happens when the electron moves from the first energy level to the second energy level?
Energy is absorbed, and an emission line is produced.
Energy is released, and an emission line is produced.
Energy is absorbed by the atom.
Energy is lost from the atom.
Which statements about Earth’s core help explain Earth’s magnetic field? Check all that apply.
Earth’s core is composed of magnets.
The inner core is solid.
The outer core is solid.
The inner core is liquid and moving.
The outer core is liquid and moving.
Earth’s core is composed of iron and nickel.
Answer:
The inner core is solid.
The outer core is liquid and moving.
Earth’s core is composed of iron and nickel.
Explanation:
Convection currents are produced in the outer liquid core. This motion together with the Earth's rotation creates a system of electrical currents, since it is composed of metals such as iron and nickel. The magnetic fields generated by the electric currents align, creating the Earth's magnetic field. The solid inner core acts as a stabilizer of the magnetic field generated by the liquid outer core.
Two friends, Joe and Sam, go to the gym together to strength train. They decide to start off with an exercise called flat bench press. Lying flat on a bench with their arms in an extended position, they slowly lower (to their chest) and then raise a barbell back to the starting position. They start off by using a 45.0 kg barbell. Joe is taller than Sam which means Joe\'s arms are 69.4 cm long while Sam\'s are 60.6 cm. Calculate the work done by Joe, WJoe, when he raises the barbell to finish one repetition. The acceleration due to gravity is 9.81 m/s3
A 70kg divers steps off of a 10m tower and drops from rest straight into the water. If he comes to rest 5m beneath the surface, determine the average resistance force exerted on him by the water.
First, we need to calculate the total distance that the diver travelled. The diver jumped off a 10-meter tower and went 5 meters under the water. Therefore, the total distance travelled by the diver is 10 meters (from the tower) plus 5 meters (underwater), which equals 15 meters.
Next, we will determine the work done on the diver. The work done is equal to the change in potential energy, which can be calculated by multiplying the diver's mass by gravity and then by the total distance the diver travelled. Given that the diver's mass is 70kg and the acceleration due to gravity is 9.8m/s², the work done is 70kg * 9.8m/s² * 15m, which equals 10290 Joules.
Finally, we'll find the average resistance force exerted on the diver by the water. The work done on the diver is also equal to the average force times the distance. Therefore, the average force is the work done divided by the distance. When you divide the work done (10290 Joules) by the total distance travelled (15 meters), you get an average force of 686 Newtons.
Hence, the total distance travelled by the diver in water is 5 meters, the work done on the diver is 10290 Joules, and the average resistance force exerted on the diver by the water is 2058 Newtons.
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A mass m = 4.6 kg hangs on the end of a massless rope L = 2.16 m long. The pendulum is held horizontal and released from rest.
1)How fast is the mass moving at the bottom of its path?2)What is the magnitude of the tension in the string at the bottom of the path?
ind the velocity my using the conservation of energy mgh=1/2mv^2. At the bottom, the mass is turning in a circle with tension pointing up towards the center of the circle and weight pointing down. Use the centripetal force requirement mv^2/r=T-W and solve for T. Hope this helps.
The speed of the mass at the bottom of its path is approximately 6.51 m/s, and the tension in the string at that point is approximately 141.4 N, which is calculated using the conservation of energy and understanding the forces in a circular motion.
To solve both parts of the problem involving the mass hanging on the end of a massless rope and released from rest, we apply principles of physics, specifically conservation of energy and dynamics of a simple pendulum. Conservation of energy tells us that the potential gravitational energy at the top is converted to kinetic energy at the bottom of its path. The tension in the string at the bottom can be calculated by understanding the forces acting on the mass at that point, which include the centripetal force necessary to maintain its circular path and the gravitational force pulling it downward.
Using conservation of energy, we have:
Potential Energy at top (U): U = mgh = mgL
Kinetic Energy at bottom (K): K = 1/2 m[tex]v^2[/tex]
Setting U equal to K gives us:
mgL = 1/2 m[tex]v^2[/tex]
From which we can solve for v, the speed at the bottom:
v = [tex]\sqrt{2gL}[/tex]
Substituting in the values (g = 9.8 m/[tex]s^2[/tex], L = 2.16 m),
v = [tex]\sqrt{2 \times 9.8 \times 2.16} = \sqrt{42.336} \approx 6.51 m/s[/tex]
The tension in the string (T) at the bottom is the sum of the gravitational force and the centripetal force required to keep the mass moving in a circle:
T = mg + m[tex]v^2[/tex]/L
Substituting in the known values:
T = 4.6 × 9.8 + 4.6 × [tex](6.51)^{2/2.16}[/tex]
T = 45.08 + 4.6 × (42.3961)/2.16
T = 45.08 + 96.3273
T = 141.4073 N
The tension at the bottom of the path is approximately 141.4 N.
What is the sequence of energy transformations associated with a hydroelectric dam?
A force of 400 Newtons stretches a spring 2 meters. A mass of 50 kilograms is attached to the end of the spring and is initially released from the equilibrium position with an upward velocity of 10 m/s. After finding the equation of motion, calculate x(t = pi/12).
Fill in the blank:energy can never be created or destroyed, just ------- or --------
Help!!!! Please..... Someone. Problem:
Starting with an initial speed of 5.00 m/s at a height of h = 0.260 m, the m1 = 1.55 kg ball swings downward and strikes the m2 = 4.50 kg ball that is at rest, as the drawing shows.
(a) Using the principle of conservation of mechanical energy, find the speed of the 1.55-kg ball just before impact.
(b) Assuming that the collision is elastic, find the velocities (magnitude and direction) of both balls just after the collision.
(c) How high does each ball swing after the collision, ignoring air resistance? ...?
Answer:
Part a)
[tex]v_f = 5.48 m/s[/tex]
Part b)
[tex]v_1 = -2.67 m/s[/tex]
[tex]v_2 = 2.81 m/s[/tex]
Part c)
[tex]h_1 = 0.36 m[/tex]
[tex]h_2 = 0.40 m[/tex]
Explanation:
Part a)
As we know by energy conservation law
initial kinetic energy + initial potential energy = final kinetic energy + final potential energy
So here we know that
[tex]\frac{1}{2}mv_i^2 + mgh_i = \frac{1}{2}mv_f^2 + mgh_f[/tex]
[tex]v_i = 5 m/s[/tex]
[tex]h_i = 0.260 m[/tex]
[tex]h_f = 0[/tex]
now we have
[tex]v_f^2 = v_i^2 + 2gh[/tex]
[tex]v_f^2 = 5^2 + 2(9.8)(0.260)[/tex]
[tex]v_f = 5.48 m/s[/tex]
Part b)
As we know that collision is perfectly elastic collision
so we will have
[tex]m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}[/tex]
[tex]1.55(5.48) + 0 = 1.55 v_1 + 4.50 v_2[/tex]
also we know for elastic collision
[tex]v_2 - v_1 = 5.48[/tex]
[tex]v_1 = -2.67 m/s[/tex]
[tex]v_2 = 2.81 m/s[/tex]
Part c)
Now the height of each ball is given by
[tex]h = \frac{v^2}{2g}[/tex]
[tex]h_1 = \frac{2.67^2}{2(9.81)}[/tex]
[tex]h_1 = 0.36 m[/tex]
[tex]h_2 = \frac{2.81^2}{2(9.81)}[/tex]
[tex]h_2 = 0.40 m[/tex]
The student's question involves applying the conservation of mechanical energy to find the speed of a ball before impact, using the conservation of momentum and kinetic energy for an elastic collision, and determining the height of the swing post-collision in physics.
Explanation:To solve the student's problem, we will apply the principles of conservation of mechanical energy and conservation of momentum which are fundamental concepts in physics, specifically in the field of mechanics. Given the nature of the questions, this falls into the category of a high school physics problem, typically encountered by students learning about motion and energy.
Conservation of Mechanical EnergyFor part (a), the conservation of mechanical energy states that the total mechanical energy (kinetic plus potential) in an isolated system remains constant if only conservative forces are acting. Initial mechanical energy at the height h will be equal to the kinetic energy just before the impact.
Elastic CollisionFor part (b), an elastic collision is one where both momentum and kinetic energy are conserved. We would apply both the conservation of momentum and kinetic energy equations to find the velocities of the two balls post-collision.
Height of Swing After CollisionFor part (c), after the collision, to find how high each ball swings, we would convert the kinetic energies of the balls just after the collision to potential energies at the peak of their respective swings, assuming no energy is lost to air resistance.
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When an electric current passes through water, _____ takes place, breaking down the compound into hydrogen and oxygen.?
Turner’s treadmill starts with a velocity of
−2.7 m/s and speeds up at regular intervals
during a half-hour workout.After 33 min, the
treadmill has a velocity of −7.1 m/s.
What is the average acceleration of the
treadmill during this period?
Answer in units of m/s
...?
33 60
---
1980 33*60sec = 1980 sec for comparison
By definition, we have to:
[tex] vf = a * t + vo
[/tex]
Where,
vf: final speed
vo: initial speed
t: time
a: acceleration
Clearing the acceleration we have:
[tex] a = \frac{vf-vo}{t}
[/tex]
When replacing values we have to take into account two things:
1) Assume that the given speeds are positive
2) The time must be in seconds
The time in seconds is:
[tex] t = 33 * 60
t = 1980
[/tex]
Then, replacing values we have:
[tex] a =\frac{7.1-2.7}{1980}
[/tex]
[tex] a = 0.002 \frac{m}{s ^ 2}
[/tex]
Answer:
The average acceleration of the treadmill during this period is:
[tex] a = 0.002 \frac{m}{s ^ 2}
[/tex]
J is the midpoint of The coordinates of J are (-8,7) and the coordinates of K are (3,4) find the coordinates of L. can someone help me? i get really confused with geometry and im trying to finish this final and im not sure how to solve this problem ...?
T/F:Most of the energy we use today comes from renewable sources.
An artillery shell is fired at an angle of 62.7
above the horizontal ground with an initial
speed of 1520 m/s.
The acceleration of gravity is 9.8 m/s2 .
Find the total time of flight of the shell,
neglecting air resistance.
Answer in units of min ...?
To find the total time of flight of the artillery shell, we can use the kinematic equation for vertical motion. By calculating the vertical component of the initial velocity and plugging in the known values, we can solve for the time of flight. Finally, we can convert the time to minutes by dividing by 60.
Explanation:To find the total time of flight of the shell, we can use the kinematic equation for vertical motion: d = v0yt + 0.5gt2. In this equation, d represents the vertical displacement of the shell (which is 200 m), v0y represents the vertical component of the initial velocity (which can be found using v0y = v0sin(θ)), t represents the time of flight, and g represents the acceleration due to gravity.
Since the shell is fired at an angle of 62.7° above the horizontal, the vertical component of the initial velocity can be calculated as v0y = 1520 m/s * sin(62.7°). Plugging in the known values, we can solve for t.
Once we have the time of flight, we can convert it to minutes by dividing by 60 (since there are 60 seconds in a minute).
The following graph shows the rates of decay for four parent isotopes. Based on the graph, which parent isotope most likely has a half-life of 13 billion years?
A
B
C
D
Answer:
A or B (mostly A)
Explanation:
After 14 billion years, approximately 85% of the original parent isotope will still exist, compared to roughly 45% of parent isotope C, 12.5% of parent isotope B, and nearly none of the parent isotope A!
We know curve D represents the parent isotope with the longest half-life, and curve A represents the parent isotope with the shortest half-life!
We also know it cannot be D or C. So we are stuck with curves B and A! However, since parent isotope B has 12.5% parent isotopes left after 14 billion years(1billion years before the year we are talking about), and nearly none of the parent isotope A is left, this leads me to beleive that the answer is curve, or parent isotope, A!
I am sorry if i am wrong though.
Have a marvelous day!