Given that,
The initial height of the projectile, y₀=40 m
The initial velocity of the projectile, v₀=4.47 m/s
The direction of the initial velocity is parallel to the ground. Therefore the x-component of the initial velocity v₀x=4.47 m/s.
And the y-component of the initial velocity is v₀y=0 m/s
From the equation of the motion we have,
[tex]y=y_0+v_{0y}t+\frac{1}{2}gt^2[/tex]Where y is the final height of the projectile which is zero as it finally hits the ground. And g =-9.8m/s² is the acceleration due to gravity. And t is the time interval of the flight of the projectile.
On substituting the known values in the above equation,
[tex]\begin{gathered} 0=40+0+\frac{1}{2}\times-9.8\times t^2 \\ =40-4.9t^2 \end{gathered}[/tex]On rearranging the above equation and simplifying it,
[tex]\begin{gathered} t=\sqrt{\frac{40}{4.9}} \\ =2.86\text{ s} \end{gathered}[/tex]The x-component of the velocity remains constant as there is no acceleration in that direction.
The horizontal distance travelled or the range of the projectile can be calculated using the formula,
[tex]R=v_{0x}t[/tex]On substituting the known values in the above equation,
[tex]R=4.47\times2.86=12.78\text{ m}[/tex]Therefore the projectile will land 12.78 meters away
why is scientific notation used ?a. to round numbers to the nearest whole numberb. to promote reproducibility of datac. to increase the validity of datad. to express very large or very small numbers
Scientific notation is used to represent very large or very small numbers in a simple way.
Therefore, the answer is option D.
Find the following for path C in the figure below (a) the total distance traveledm(b) the distance from start to finishm(c) the displacement from start to finishm
(a). The total distance traveled in the path C is,
[tex]\begin{gathered} D=\text{ From 2 m to 10 m + from 10 m to 8 m + from 8 m to 10 m} \\ =\mleft(10-2\mright)+\mleft(10-8\mright)+\mleft(10-8\mright) \\ =8+2+2 \\ =12\text{ m} \end{gathered}[/tex]Thus, the total distance traveled in the path C is 12 m.
(b). The distance from the start (2 m) to the finish (10 m) is,
[tex]\begin{gathered} d=\text{from 2 m to 10 m} \\ d=10-2 \\ d=8\text{ m} \end{gathered}[/tex]Thus, the distance traveled from start to finish is 8 m.
(c). The displacement from the start (2 m) to the finish (10 m) by neglecting the return travel in the path C is,
[tex]\begin{gathered} d^{\prime}=10-2 \\ d^{\prime}=8\text{ m} \end{gathered}[/tex]Thus, the displacement for the path C is 8 m.
The volume of gas v held at a constant temperature in a closed container varies inversely with it's pressure P. If the V of gas is 1600 cm^3 when the P is 250 mm Hg, find the v when the P is 400 mm Hg?
Explanation
The volume of gas v held at a constant temperature in a closed container varies inversely with it's pressure P,in math terms it is
[tex]\begin{gathered} V\propto\frac{1}{P} \\ where\text{ V is the volume} \\ P\text{ is the presion} \end{gathered}[/tex]When Pressure is constant, Volume is directly proportional to temperature.
Step 1
given the data, we need to apply the formula for a constant temperature ,
[tex]\begin{gathered} V_2=\frac{P_1V_1T_2}{T_1P_2} \\ as\text{ the temperature is constatn} \\ V_2=\frac{P_1V_1}{P_2} \end{gathered}[/tex]so
[tex]\begin{gathered} V_2=\frac{250\text{ mmHg*1600 cm}}{400} \\ V_2=1000\text{ cm}^3 \end{gathered}[/tex]so, the answer is
[tex]1000\text{ cm}^3[/tex]I hope this helps you
The siren of a burglar alarm system has a frequency of 960Hz . During a patrol a security officer, traveling in his car , hears the siren of the alarm of a house and approaches the house at a constant velocity. A detector in his car registers the frequency of the sound as 1000 Hz . Calculate the speed at which the patrol car approaches the house . Use the speed of sound in air as 340m.s
Answer:
14.2 m/s
Explanation:
When the source and receiver are getting closer, we can use the following equation:
[tex]f_o=(\frac{v+v_o}{v-v_s})f_s[/tex]Where fo is the observed frequency, fs is the emitted frequency, vo is the speed of the observed, vs is the speed of the source, and v is the speed of the sound. Solving for vo, we get:
[tex]\begin{gathered} \frac{f_o}{f_s}=\frac{v+v_o}{v-v_s} \\ \\ \frac{f_o}{f_s}(v-v_s)=v+v_o \\ \\ \frac{f_o}{f_s}(v-v_s)-v=v_o \\ \\ v_o=\frac{f_o}{f_s}(v-v_s)-v \end{gathered}[/tex]Then, replacing v = 340 m/s, vs = 0 m/s, fs = 960 Hz, and fo = 1000 Hz, we get:
[tex]\begin{gathered} v_r=\frac{1000}{960}(340-0)-340 \\ \\ v_r=14.2\text{ m/s} \end{gathered}[/tex]Therefore, the speed of the patrol car is 14.2 m/s
An object is placed 10.0 cm in front of a thin concave lens with a focal length of 18 cm. Calculate the imageposition
The focal length of a concave lens is expressed as,
[tex]\frac{1}{f}=\frac{1}{u}+\frac{1}{v}[/tex]Here, f is the focal length, u is the distance of object and v is the distance of image.
Plug in the known values,
[tex]\begin{gathered} \frac{1}{18\text{ cm}}=\frac{1}{10.0\text{ cm}}+\frac{1}{v} \\ \frac{1}{v}=\frac{1}{18\text{ cm}}-\frac{1}{10.0\text{ cm}} \\ v=\frac{(18\text{ cm)(10.0 cm)}}{10.0\text{ cm-18 cm}} \\ =-22.5\text{ cm} \end{gathered}[/tex]Thus, the distance of image is -22.5 cm where negative sign indicates that the image will be at the same side of object.
an7. Pressure is calculated by dividing force by theover which the force is exerted.Which state of matter will hold its shape without a container?QPressure is calculated by dividing force by the “what”over which the force is exerted?
The pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Then, the missing word is area.
How does the velocity of a falling object change with time? How would you describe the mathematical relationship between velocity and time of a falling object? Explain the answer using your data, graphs, and the kinematic equations.The image below shows the ball stopping at 2 4 6 8 and 10 and how long it took it too stop there
We will have the following:
First, we can see that the data presented is the following:
Now, from this information we can construct the following graphical relationship between time and distance drawn by the object:
From this we can infer that the relationship between time and distance is linear in nature, and the path of best descripton by linear regression is given by:
Where the approximation is:
[tex]f(x)=2.47204029x-0.4796893103[/tex]We can see the linear relationship that fits the model, from this and the fact that in kinematics the following is true:
[tex]d=v\ast t[/tex]Where "d" is the distace, "v" is the velocity and "t" the time.
From the data, the values of "x" represent the time and thus, the ratio of the function found is the velocity of the object.
In summary, the relationship is linear as per in kinematics, time and distace change proportionally in the data provided; and the approximated velocity of the object was 2.47m/s.
URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!!
Answer:
it’s the last one chemical covered to mechanical
Explanation:
asked my science teacher to make sure it’s correct
A 0.7kg ball Is thrown and accelerated by 62 m/s. How much force is applied to it? Round your answer to the nearest whole number
Given:
the mass of the ball is m=0.7 kg.
The acceleration in the ball is
[tex]a=62\text{ m/s}^2[/tex]Required: the force applied on the ball
Explanation:
The force is given by
[tex]F=ma[/tex]here, F is force, m is the mass, and a is the acceleration.
Plugging all the values in the above relation, we get:
[tex]\begin{gathered} F=0.7\text{ kg}\times62\text{ m/s}^2 \\ F=43.4\text{ N} \\ F\approx43\text{ N} \end{gathered}[/tex]Thus, the force on the ball is 43 N.
You want to know the intensity of electric current whose total charge is 35 Coulombs, calculate the intensity if this charge is passed through copper for 7 seconds
ANSWER
[tex]5A[/tex]EXPLANATION
To find the current intensity, we have to apply the formula for current intensity:
[tex]I=\frac{q}{t}[/tex]where q = charge
t = time
Hence, the current intensity is:
[tex]\begin{gathered} I=\frac{35}{7} \\ I=5A \end{gathered}[/tex]That is the answer.
On what behavior of matter does mercury in a glass thermometer depend?Select one:a. Change of color when heated.b. Change of state when heated.c. Change of size when heated. d. Change of mass when heated.
Since mercury expands with temperature a glass thermometer depends on the change of size when heated, therefore, the answer is c.
Consider a 0.9 kg object traveling in a circle of radius 6 meters. The object completes 1 circles in 2 seconds traveling at constant speed. What net force is required to sustain this motion? [Hint: 2 is almost equal to 10.]
Mass of the object, m= 0.9 kg and radius of the circular path, r = 6 m and time, T = 2 seconds.
Here, the velocity will be
[tex]\begin{gathered} v=\frac{dis\tan ce}{time} \\ =\frac{2\pi r}{T} \end{gathered}[/tex]The force required to sustain this motion is
[tex]F=\frac{mv^2}{r}[/tex]Substituting the value of velocity, we get
[tex]\begin{gathered} F=\frac{m(2\pi r)^2}{rT^2} \\ =\frac{4m\pi^2r}{T^2} \\ =\frac{4\times0.9\times10\times6}{2^2} \\ =54\text{ N} \end{gathered}[/tex]
Ball A of mass mA = 3 kg moves to the right (positive direction) with a velocity 4 m/s, while ball B moves to the left (negative direction) with a velocity -4 m/s. After the collision, A's velocity is -21 m/s and B's velocity is 1 m/s. What is the mass of B?
Given:
The mass of A is,
[tex]m_A=3\text{ kg}[/tex]The initial velocity of A is,
[tex]u_A=4\text{ m/s}[/tex]The initial velocity of B is,
[tex]u_B=-4\text{ m/s}[/tex]The final velocity of A is,
[tex]v_A=-21\text{ m/s}[/tex]The final velocity of B is,
[tex]v_B=-1\text{ m/s}[/tex]Applying the momentum conservation principle we can write,
[tex]\begin{gathered} m_Au_A+m_Bu_B=m_Av_A+m_Bv_B \\ 3\times4+m_B(-4)=3\times(-21)+m_B\times1 \\ 12-4m_B=-63+m_B \\ 5m_B=75 \\ m_B=15\text{ kg} \end{gathered}[/tex]Hence, the mass of B is 15 kg.
What is one way that the gravitational force between the moon and the earth would increase?a. If the size of the moon decreased while the distance remained constant.b. If the size of the moon increased while the distance remained constantc. If the size of the earth increased while the distance remained constant.d. both b and c
Answer:
d. both b and c
Explanation:
If the mass of either object increases, the gravitational attraction between them increases.
F = G m1*m2 / r^2
Where:
F: Force
G = constant
m = masses
r = distance between objects
Mass is directly proportional to the gravitational force.
Please help with the following question.Mass of cylinder = m0
Given:
Mass of block = m0
Mass of cylinder = m0
Given that a cylinder is placed at the top of an incline and the block is also placed at the top of a separate rough incline.
Given that both objects reach the bottom of their respective inclines with the same translational speed, let's explain why.
Since the mass of the cylinder and mass of the block are the same, both objects can be said to be rolling down their respective inclines downward along the smooth slope due to the acceleration due to gravity.
In this case the downward acceleration of the cylinder will be higher than that of the block. Although the acceleration of the block should be higher due to the rotational inertia. This happens because the block is exposed to a higher frictional level(due to its rough incline) which causes it to slow down, hence its acceleration will now be apparently the same with that of the cylinder.
In this case, we now have equal initial velocities, equal masses, and equal acceleration.
Since these units are the same, both the block and the cylinder will have reach the bottom of their inclines with the same translational speed.
We have the figure below:
Harmonics are multiples of the fundamental. If the fundamental frequency is 53 Hz, with what frequency will the 8th harmonic resonate?
Take into account that the relation in betwee the fundamental and the harmonics is given by:
f = fo·n
where f is the frecuency of the nth harmonic and fo is the fundamental.
Then, for the 8th harmonic (n = 8) and a fundamental of 53 Hz, you obtain for f:
f = (53 Hz)(8)
f = 424 Hz
Hence, the frequency of the 8th harmonic is 424 Hz
Two boats start together and race across a 42-km-wide lake and back. Boat A goes across at 42 km/h and returns at 42 km/h. Boat B goes across at 21 km/h, and its crew, realizing how far behind it is getting, returns at 63 km/h. Turnaround times are negligible, and the boat that completes the round trip first wins.(a) Which boat wins?o Boat Ao Boat Bo It's a tie(b) By how much?_____ km(c) What is the average velocity of the winning boat?_____ km/h
ANSWER
[tex]\begin{gathered} (a)\text{ Boat A} \\ \\ (b)\text{ }42\text{ km} \\ \\ (c)\text{ }0\text{ km/h} \end{gathered}[/tex]EXPLANATION
(a) To determine which boat wins, we have to find the total time the journey takes for each boat.
To do that, apply the formula for speed:
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ t=\frac{d}{s} \end{gathered}[/tex]where d = distance traveled
t = time taken
For boat A, the time taken to go across and return is:
[tex]\begin{gathered} t=\frac{42}{42}+\frac{42}{42}=1+1 \\ \\ t=2\text{ hrs} \end{gathered}[/tex]For boat B, the time taken to go across and return is:
[tex]\begin{gathered} t=\frac{42}{21}+\frac{42}{63}=2+0.667 \\ \\ t=2.667\text{ hrs} \end{gathered}[/tex]We see that it takes boat B longer to complete the race. Hence, boat A will win the race.
(b) To determine how much boat A will win, we can look at the distances both boats cover. Notice that while getting across the lake, boat A travels twice as fast as boat B and travels at the same speed while returning.
This implies that in the time that boat A travels both laps of the race, boat B is just reaching the other end of the lake.
In other words, in the time that boat A travels 84 km, boat B travels 42 km.
Hence, boat A will beat boat B by a distance of:
[tex]\begin{gathered} 84-42\text{ km} \\ \\ 42\text{ km} \end{gathered}[/tex](c) In the race, the winning boat starts from one end of the lake, gets to the other end, and then, returns to the starting point.
This implies that the displacement of the boat is 0 km.
Velocity is given by dividing displacement by the time taken. Since the displacement is 0 km, the velocity of the winning boat, Boat A is 0 km/h
5. Object A has a mass of 3 kg and is moving at 6 m/s before the collision with the 2 kg object B which is moving at -5 m/s. After the collision, object A has a velocity of 2 m/s. a. What is the total initial momentum of object A and B?b. What is the final velocity of object B after the collision?
Given,
The mass of object A is
[tex]m_1=3kg[/tex]The mass of object B is
[tex]m_2=2kg[/tex]The velocity of the object A before the collision is
[tex]u_1=6\text{ m/s}[/tex]The velocity of the object B before the collision is
[tex]u_2=-5\text{ m/s}[/tex]The velocity of object A after the collision is
[tex]v_1=2\text{ m/s}[/tex]Let the velocity of object B after the collision is v.
(a) The total initial momentum of objects A and B.
[tex]\begin{gathered} m_1u_1+m_2u_2=(3kg)\times(6\text{ m/s)+(2 }kg)\times(-5\text{ m/s)} \\ =18-10 \\ =8 \end{gathered}[/tex]The total initial momentum of objects A and B is 8.
(b) From the conservation of momentum,
[tex]\begin{gathered} m_1u_1+m_2u_2=m_1v_1+m_2v_2 \\ 8=(3kg)\times(2\text{ m/s)+(2 }kg)\times v \\ 2v=8-6 \\ v=1\text{ m/s} \end{gathered}[/tex]The final velocity of object B after the collision is 1 m/s.
Hello could you please help me with this question? is parallel to the y-axis and has an x-intercept of 3
Answer:
[tex]x=3[/tex]Explanation: We need to find the equation of a line that is parallel to the y-axis and has an x-intercept of 3:
This simply implies that the slope is infinite, and so the equation must be:
[tex]x=3[/tex]The plot of the equation:
NOTE! The plot matches the description of the problem.
help please asap !looking for the answer to number 1 Its assigned homework for online that I don’t understand
Let's explain what a simple machine is.
Definition:
A simple machine can be defined as a mechanical device used for applying force and doing work.
It changes the direction and magnitude of force.
In a simple machine there is no combination of parts and they have very few movable parts.
Types of Simple machines:
• Screw
,• Pulley
,• Wedge
,• Wheel and axel
,• Lever
,• Inclined plane
Example of Screw is a screw.
Example of a pulley is an elevator
Example of a wedge is
A car accelerates from from 20m/s to 30m/s in 10s (a) calculate the cars acceleration using v = u+at (b) Draw a velocity-time graph to show the cars motion find the distance it travels by calculating the area under the graph (c) check your answer by using the equation s = ut+1/2seqore
a.
The cars acceleration is given as
V = u +at
30 = 20 + a * 10
30- 20 = 10*a
acceleration = 1 m/s²
b. The velocity time graph is shown below:
Distance covered (s)= Area under the curve=
20 x 10 + [ (1/2) x 10 x 10 ]
distance = 250 m
C. checking answer
s = ut + (1/2) x at²
s = 20 x 10 + [ (1/2) x 10 x 10 ]
s = 250 meters.
What is acceleration?
Acceleration is described as the rate of change of the velocity of an object with respect to time.
The Velocity-time graph is a plot between Velocity and Time that shows the Motion of the object that moves in a Straight Line. It is given that the magnitude of Velocity at a given instant is equal to its Instantaneous Speed.
On a velocity-time graph a horizontal (flat) line indicates the object is travelling at a constant speed while a straight diagonal line indicates that the object's velocity is varying.
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You deposit $2000 in an account earning 8% interest compounded monthly. How much will you have in the account in 5 years?
The amount in my account after 5 years, if a deposit $2000 will be $2985.62.
What is compound interest?Compound interest is the interest calculated on the principal and the interest accumulated over the previous period.
Tocalculate the amount, that will be in my account in 5 years, we use the formula below.
Fromula:
A = P(1+R/100n)ⁿˣ............... Equation 1Where:
A = AmountP = PrincipalR = Ratex = Timen = Total number of months in a yearFrom the question,
Given:
P = $2000R = 8%n = 12 monthsx = 5 yearsSubstitute these values into equation 1
A = 2000[1+8/(12×100)]⁵*¹²A = 2000(1+0.0067)⁶⁰A = 2000(1.0067)⁶⁰A = $2985.62Hence, the amount in my account will be $2985.62.
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What is the total motion of an object along a path? Questions Time Distance Motion Displacement
The total motion of an object along a path is total distance covered in the given time.
What is motion?The phenomenon of an item changing its position with respect to time is known as motion in physics. In mathematics, displacement, distance, velocity, and acceleration are used to explain motion.
Motion is total distance covered or the displacement covered in the given time.
To learn more about motion refer to the link:
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(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 3.9% of their strength? %(b) How many percent would the current need to be increased to return the torque to original values? %
a) The torque of a DC motor is directly proportional to the flux of the magnetic field, thus, when we reduce the flux (strength of permanent magnet) by 3.9%, we also reduce the torque by 3.9%
b) The torque of the DC motor can also be written as T=k*phi*I, where I is the current on the static part of the assembly. Thus, in order to maintain this relation, if the new phi is 0.961 times the old phi, the new current will need to be 1/0.961 times the old current, and thus 4% higher
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Answer:
u nor get work at all just dey post..
The small piston of a hydraulic press has an area of 3.2 in2. If the applied force is 2.0 lb, what must the area of the large piston be to exert a pressing force of 795 lb?
Given data:
The area of the hydraulic press is,
[tex]A_1=3.2in^2[/tex]The applied force is,
[tex]F_1=2\text{ lb}[/tex]The pressing force on the large piston is
[tex]F_2=795\text{ lb}[/tex]Given hydraulic press works on Pascal's law principle.
From the Pascal's law, the equation can be given as,
[tex]\frac{F_1}{A_1}=\frac{F_2}{A_2}[/tex]Here,
[tex]A_2[/tex]is the area of the larger piston.
Substituting the values in the above equation, we get:
[tex]\begin{gathered} \frac{2\text{ lb}}{3.2in^2}=\frac{795\text{ lb}}{A_2} \\ A_2=1272in^2 \end{gathered}[/tex]Thus, the area of the large piston is
[tex]1272in^2[/tex]A 25 kg mass is thrown from the ground to a height of 50 m. (a) find the kineticenergy of the mass at this height.; (b) find the potential energy of the mass at thisheight. ; (C) find the velocity of the mass when it reach the ground.
Given
m: mass
m = 25 kg
h: height
h = 50 m
Procedure
(a) Kinetic energy is directly proportional to the mass of the object and to the square of its velocity. At this height initial velocity is equal to zero
K = 0 J
(b) The potential energy of any given object is a measurement of its potential to do work, create heat and generate power.
[tex]\begin{gathered} U=mgh \\ U=25\operatorname{kg}\cdot9.8m/s^2\cdot50m \\ U=12250\text{ J} \end{gathered}[/tex](c) When the mass reaches the ground all the potential energy is transformed into kinetic energy.
[tex]\begin{gathered} \frac{1}{2}mv^2=U \\ \frac{1}{2}mv^2=12250J \\ v=\sqrt[]{\frac{2\cdot12250}{25\operatorname{kg}}} \\ v=31.30\text{ m/s} \end{gathered}[/tex]A ball is thrown upward with a speed of 38.0 m/s from the top of a building 240 m tall.a) How long will it take for this ball to reach the ground?b) How long will it take for this ball to reach the highest point?
A) The total time it takes for the ball to reach the ground = 11.702 seconds
B) The time taken by the ball to reach the highest point = 3.8 seconds
Explanations:To get the distance from the top of the building to the maximum height reached by the ball:
[tex]v^2=u^2\text{ + 2gh}[/tex]The initial speed, u = 38 m/s
The final speed at the maximum height, v = 0m/s
g = -10m/s² (Since the ball is thrown upwards)
[tex]\begin{gathered} 0^2=38^2+2(-10)h \\ 20h\text{ = }1444 \\ h\text{ = }\frac{1444}{20} \\ h\text{ = }72.2\text{ m} \end{gathered}[/tex]The distance from the top of the building to the maximum height = 72.2 m
The time taken for the ball to reach the highest point from the top of the building will be calculated using the equation:
v = u + gt
0 = 38 + (-10)t
10t = 38
t = 38/10
t = 3.8 s
From the maximum height of the ball to the ground:
The height, H = 72.2 + 240
H = 312.2 m
The initial velocity, u = 0 m/s
g = 10 m/s²
Using the equation below:
[tex]\begin{gathered} v^2=u^2+2gH \\ v^2=0^2\text{ + 2(10)}(312.2) \\ v^2\text{ = }6244 \\ v\text{ = }\sqrt[]{6244} \\ v\text{ = }79.02\text{ m/s} \end{gathered}[/tex]The time spent from the top of the building to the the ground will be calculated using the formula:
v = u + gt
79.02 = 0 + 10t
10t = 79.02
t = 79.02/10
t = 7.902 s
The total time it takes for the ball to reach the ground = 7.902 + 3.8
The total time it takes for the ball to reach the ground = 11.702 seconds
The time taken by the ball to reach the highest point = 3.8 seconds
If the voltage between 2 plates is 10 V and they are separated by 2 m, what is the electric field? A. 10 V/m B. 5 V/m C. 2 V/m D. 20 V/mWhat does it mean when there is a straight line on a current vs voltage graph?A. Current is proportional to the Voltage squared.B. Current and Voltage are not proportional.C. Current and Voltage are directly proportional.D. Current and Voltage are inversely proportional.
1) We will have that:
[tex]E=\frac{kQ}{r^2}[/tex]So:
[tex]E=5V/m[/tex]2) We will have the following:
It would mean that:
Current and voltage are directly proportional.
Question 1001 10The device shown demonstrates which energy transformation?A Blectrical energy - electromagnetic energyB. Besteomaretic energy - Kinetic energyC. Yinetic energy-electrical energyD. Chemical energy-electromagnetic energyPlease answer this question!!
ANSWER
A. electrical energy → electromagnetic energy
EXPLANATION
The device shown is a lamp. To turn on the lamp we have to connect it to the electric power; there we have electrical energy. The lamp has a light bulb, which when it's on it emits light. Remember that light is an electromagnetic wave. Therefore the electrical energy is transformed into electromagnetic energy.