A soccer ball is kicked from the top of one building with a height of H1 = 30.2 m to another building with a height of H2 = 12.0 m.
The ball is kicked with a speed of v0 = 15.10 m/s at an angle of θ = 74.1° with respect to the horizontal. The mass of a size 5 soccer ball is m = 450 g. When the ball lands on the other building, its speed is 19.89 m/s.
How much energy was lost to air friction? The ball is kicked without a spin.
The amount of energy lost to air friction, given the data is 37.71 J
How to obtain the initial energyInitial velocity (u) = 15.1 m/sMass (m) = 450 g = 450 / 1000 = 0.45 KgInitial Energy (E₁) = ?
E₁ = ½mu²
E₁ = ½ × 0.45 × 15.1²
E₁ = 51.3 J
How to obtain the final energyFinal velocity (u) = 19.89 m/sMass (m) = 450 g = 450 / 1000 = 0.45 KgFinal Energy (E₂) = ?
E₂ = ½mv²
E₂ = ½ × 0.45 × 19.89²
E₂ = 89.01 J
How to determine the energy lostInitial Energy (E₁) = 51.3 JFinal Energy (E₂) = 89.01 JEnergy lost =?Energy lost = E₂ - E₁
Energy lost = 89.01 - 51.3
Energy lost = 37.71 J
Learn more about energy:
https://brainly.com/question/10703928
#SPJ1
There is a current of 0.83 A through a lightbulb in a 120 V circuit. What is the resistance of this lightbulb?
Considering the Ohm's law, the resistance of the lightbulb is 144.58 Ω.
Definition of currentThe flow of electricity through an object, such as a wire, is known as current (I). Its unit of measure is amps (A). So the current is a measure of the speed at which the charge passes a given reference point in a specified direction.
Definition of voltageThe driving force (electrical pressure) behind the flow of a current is known as voltage and is measured in volts (V) (voltage can also be referred to as the potential difference or electromotive force). That is, voltage is a measure of the work required to move a charge from one point to another.
Definition of resistanceResistance (R) is the difficulty that a circuit opposes to the flow of a current and it is measured in ohms (Ω).
Ohm's lawOhm's law establishes the relationship between current, voltage, and resistance in an electrical circuit.
This law establishes that the intensity of the current that passes through a circuit is directly proportional to the voltage of the same and inversely proportional to the resistance that it presents.
Mathematically, Ohm's law is expressed as:
[tex]I=\frac{V}{R}[/tex]
Where:
I is the current measured in amps (A).V the voltage measured in volts (V).R the resistance that is measured in ohms (Ω).Resistance of the lightbulbIn this case, you know that the voltage between two points in a circuit is 120 V and there is a current of 0.83 A.
Replacing in the Ohm's Law:
[tex]0.83A=\frac{120 V}{R}[/tex]
Solving:
0.83 A× R= 120 V
[tex]R=\frac{120 V}{0.83A}[/tex]
R= 144.58 Ω
Finally, the resistance of the lightbulb is 144.58 Ω.
Learn more about Ohm's law:
brainly.com/question/13076023
brainly.com/question/17286882
brainly.com/question/2275770
#SPJ1
Suppose the mass of a fully loaded module in which astronauts take off from the Moon is 10,600 kg. The thrust of its engines is 25,500 N. (Assume that the gravitational acceleration on the Moon is 1.67 m/s2.)
(a) Calculate its magnitude of acceleration in a vertical takeoff from the Moon.
m/s2
(b) Could it lift off from Earth? If not, why not?
Yes, the thrust of the module's engines is equal to its weight on Earth.
No, the thrust of the module's engines is equal to its weight on Earth.
No, the thrust of the module's engines is less than its weight on Earth.
Yes, the thrust of the module's engines is greater than its weight on Earth.
If it could, calculate the magnitude of its acceleration. (If not, enter NONE.)
m/s2
(a) The magnitude of acceleration in a vertical takeoff from the Moon will be 0.73 m/s².
(b)Option d is correct.
What is force?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 of a fully loaded module,m = 10,600 kg
Acceleration due to gravity on moon,g = 1.67 m/s²
Thrust of its engines is,F= 25,500 N.
The net force is found as follows;
[tex]\rm F_{net} = F -W[/tex]
ma = F-W
(10,600) kg × a = 25,500 N - (10,600 kg )(1.67)
a = 0.73 m/s²
b)
Yes, it lifts off from Earth. Because the thrust of the module's engines is greater than its weight on Earth.
F>W
Hence option d is correct.
To learn more about the force refer to the link;
https://brainly.com/question/26115859#SPJ1
#SPJ1
Which statement best explains the movement of electric current from the clouds to the ground during a lightning storm?
The statement that best explains the movement of electric current is that the ground is positively charged and the clouds are negatively charged.
What is lightning storm?Lightning storm can be defined as the electrical outlet that occurs due to unsteadiness of the storm clouds and the ground.
Lightning storm occurs when opposite charges build up enough in the air leading to rapid discharge of electricity.
Learn more about storms here:
https://brainly.com/question/25775340
#SPJ1
The stem of thermometer is made by thick glass and the bulb is made by thin glass, Why?
Answer:
The reason is to allow the thermometer to respond relatively quickly, and relatively accurately. The glass contains the liquid being used in the thermometer, but if it is too thick, then it will not pass heat as quickly, and it will absorb some of the heat from whatever is being measured.
Explanation:
˙˚ʚ(´◡`)ɞ˚˙
the main source of this energy is
.
Answer:motion
Explanation:
kinetic energy of an object that it possess due to its motion.
Who studied highly successful people and developed the hierarchy of needs?
A) Seligman
B) Rogers
C) Maslow
D) Zimbardo
Abraham Maslow was the person who studied highly successful people and developed the hierarchy of needs. Thus, option C is correct.
Who is Abraham Maslow?Abraham Maslow was one of the most influential psychologists of the twentieth century. His work on humanistic psychology and his development in the hierarchy of needs is very popular.
According to Abraham Maslow, humans have five tiers of needs and they are food and shelter, love and belonging, esteem, safety needs, and self-actualization.
The hierarchy of needs has five basic levels. The bottom level comprises the basic needs of people like food, and shelter. Top-level comprises esteem and self-actualization.
Maslow hierarchy of needs involves the model for understanding human behavior. Hence, Abraham Maslow developed the hierarchy of needs. Thus, the correct option is C.
To learn more about the hierarchy of needs:
https://brainly.com/question/29495620
#SPJ2
3.2 Define conservation of energy.
Answer:
A principle stating that energy cannot be created or destroyed, but can be altered from one form to another.
Explanation:
In the following circuit, C1=10.0 F, C2=2*10.0 F, C3=2*10.0 F, C4=2*9.4 F, and
C5=3*9.4. Calculate the equivalent capacitance in the circuit.
Your Answer:
The equivalent capacitance in the circuit is 15.05 F.
What is a parallel plate capacitor?The two parallel plates placed at a distance apart are used to store charge when the electric supply is on.
The capacitance of a capacitor in series is given by:
Series capacitance = 1/ capacitance 1 + 1/ Capacitance2
The capacitance of a capacitor in parallel series can be calculated as:
Parallel capacitance = Capacitance 1 + Capacitance 2
In the following circuit,
C1=10.0 F,
C2=2*10.0 F,
C3=2*10.0 F,
C4=2*9.4 F, and
C5=3*9.4.
In the circuit C2 and C3 are in parallel, their equivalent capacitance is
= 2*10.0 F+2*10.0 F
= 4 *10.0 F
Then, C1 is in series with 4 *10.0 F,
So their equivalent capacitance is
=1 /{ 1/10.0 F + 1/ 4 *10.0 F}
=0.8*10.0 F
C4 and C5 are in series, their equivalent is
=1 /{ 1/2*9.4 F + 1/3*9.4 F}
=0.75*9.4 F
Now,0.8*10.0 F and 0.75*9.4 F are in parallel.
Total equivalent capacitance is Ceq = 0.8*10.0 F + 0.75*9.4 F
Ceq = 15.05 F
Thus, the equivalent capacitance in the circuit is 15.05 F.
Learn more about parallel plate capacitors, here:
https://brainly.com/question/12733413
#SPJ1
Compare a cup of hot coffe with the Pacific Ocean . Which statement about thermal energy and temperature is correct
Pacific Ocean has more thermal energy and a higher temperature.
What is thermal energy?The term thermal energy refers to the energy that is possessed by a body as a result of a temperature difference between a body and its environment.
We know that the thermal energy is also dependent on the mass of a body. Therefore, the statement about thermal energy and temperature that is correct is; water in the Pacific Ocean has more thermal energy and a higher temperature.
Missing parts:
Compare a cup of hot coffee with the Pacific Ocean. Which statement about thermal energy and temperature is correct?
Water in the Pacific Ocean has more thermal energy and a higher temperature.
Water in the Pacific Ocean has less thermal energy and a lower temperature.
Water in the Pacific Ocean has less thermal energy and a higher temperature
Water in the Pacific Ocean has more thermal energy and a lower temperature.
Learn more about thermal energy:https://brainly.com/question/3022807
#SPJ1
Which of the following would be the magnitude of the vector given a horizontal component of 30 and a
vertical component of 40?
Answer:
50
Explanation:
Use the Pythagorean theorem to find the length of the diagonal, or the hypotenuse of an imaginary triangle. 30^2 + 40^2 = 2500, which is 50^2. So, the magnitude is 50.
Brainliest, please :)
1. Block A with a mass of 1 kg and block B with a mass of 2 kg lie on a smooth table. You wish to apply a horizontal force to each ball to give them the same horizontal acceleration (and you may safely ignore friction). Which of the following best describes the relative magnitude of the forces you must apply?
a) The magnitude of the force on block A must be twice as much as the force on block B.
b) The magnitude of the force on block B must be twice as much as the force on block A.
c) Both forces must have the same magnitude.
d) More information is needed to determine the relative magnitudes of the forces.
2. Block A has a mass of 1 kg and block B has a mass of 2 kg. Which of following best describes the relative magnitudes of the gravitational force (due to the Earth) on each block?
a)The gravitational force on block A is twice as much as the gravitational force on block B.
b)The gravitational force on block B is twice as much as the gravitational force on block A.
c)Both gravitational forces have the same magnitude.
d)More information is needed to determine the relative magnitudes of the forces.
3. You hold block A with a mass of 1 kg in one hand and block B with a mass of 2 kg in the other. You release them both from the same height above the ground at the same time. (Air resistance can safely be ignored as they fall.) Which of the following describes and explains the motion of the two objects after you release them?
a)Block A hits the ground before the block B. The same force of gravity acts on both objects, but because block A has a lower mass, it will have a larger acceleration.
b)Block B hits the ground before the block A. The larger force on block B causes it to have a greater acceleration than block A.
c)The two blocks hit the ground at the same time, because they both accelerate at the same rate while falling. The greater gravitational force on block B is compensated by its greater mass, giving it the same acceleration.
d)The two blocks hit the ground at the same time, because they both move at the same constant speed while falling. The forces on the blocks are irrelevant once they start falling.
The gravitational force on block B is twice as much as the gravitational force on block A.
What is Force?Force is the product of mass and acceleration. If the mass of A is 1Kg and the mass of B is 2Kg, In order to give the masses the same horizontal acceleration, the magnitude of the force on block B must be twice as much as the force on block A.
Given that the mass of A is 1Kg and the mass of B is 2Kg, the gravitational force on block B is twice as much as the gravitational force on block A.
If I hold block A with a mass of 1 kg in one hand and block B with a mass of 2 kg in the other and release both from the same height above the ground at the same time, the two blocks hit the ground at the same time, because they both accelerate at the same rate while falling. The greater gravitational force on block B is compensated by its greater mass, giving it the same acceleration.
Learn more about force:https://brainly.com/question/12528243
#SPJ1
can you help me? please
Answer
Yes i will help u!
A planet X moves in an elliptical path as shown below. At which point does the planet moves faster. B Assume, Ethiopian institute of space science and technology, allows to launch a space station with you. While you are in orbit, you gets thirsty. The only thing in the space station were a cup of water. you go to the cup of water and pick it up, But unfortunately your hand is twisted and the cup is turned down. Because the cup is turned down, water pour on to the floor. How would you get water?
We can get water from the sweat and exhaled breath of the people present in the space station.
How would you get water?We can get water from the sweat and exhaled breath. The water we drink is recycled from the sweat and exhaled breath of the people present in the space station which was collected through condensation on the Space Station's walls.
So we can conclude we can get water from the sweat and exhaled breath of the people present in the space station.
Learn more about water here: https://brainly.com/question/1313076
#SPJ1
Which statement best explains the movement of electric current from the clouds to the ground during a lightning storm?
The statement that best explains the movement of electric current is that the ground is positively charged and the clouds are negatively charged.
What is lightning storm?Lightning storm can be defined as the electrical outlet that occurs due to unsteadiness of the storm clouds and the ground.
Lightning storm occurs when opposite charges build up enough in the air leading to rapid discharge of electricity.
Learn more about storms here:
https://brainly.com/question/25775340
#SPJ1
Which of the following is the best hypothesis?
A. The size of ice crystals in clouds depends on the air temperature.
B. It is fun to fly an airplane through large cumulus clouds.,
C. How big can ice crystals get inside a cloud?
D. Clouds are always found in the atmosphere.
All the forces we see and experience are the result of just a few so-called fundamental forces. What are the fundamental forces in nature? Provide a brief explanation of each and an example of how we ‘see’ the forces in action.
The fundamental forces in nature are strong force, weak force, electromagnetic force, and the gravitational force.
Fundamental forces
There are four fundamental forces at work in the universe. These fundamental forces include;
The strong force: this force has strong influence or impact on objects. The weak force: this force has little impact on objects.The electromagnetic force: force due to current flowing in a conductor placed in magnetic field.The gravitational force: this is force of attraction between two objects placed in the universe.Thus, the fundamental forces in nature are strong force, weak force, electromagnetic force, and the gravitational force.
Learn more about fundamental forces here: https://brainly.com/question/793762
#SPJ1
Calculate the x and y components for the vector below. Show all work. d = 43.2 m [43.0° W of N]
The x and y components of the vector is 31.59 m and 29.46 m respectively.
X component of the vector
The x component is calculated as follows;
v(x) = v cos(43)
v(x) = 43.2 m x cos(43) = 31.59 m
Y component of the vectorThe y component is calculated as follows;
v(y) = v sin(43)
v(y) = 43.2 m x sin(43) = 29.46 m
Thus, the x and y components of the vector is 31.59 m and 29.46 m respectively.
Learn more about vectors here: https://brainly.com/question/25811261
#SPJ1
identify the solute and solvent in a solution made of 15g of oxygen and 5g
of helium
Taking into account the definition of solvent and solute, helium is the solute and oxygen is the solvent.
Definition of solute and solventThe solution is a homogeneous mixture of two or more components that have the same chemical and physical properties in a single phase. A solution is made up of two main components: the solute and the solvent.
That is, the solute and the solvent are the components of a chemical solution, that is, of a homogeneous mixture that occurs when one or more substances are dissolved in another substance.
The solute is the substance that dissolves in a solution. In solution, the solute is usually found in a lower proportion than the solvent.
Solvent is the substance in which a solute dissolves, resulting in a chemical solution. Generally, the solvent is the component that is found in the highest proportion in the solution. It will always be the solvent who will determine the state of the matter that will have the solution.
Solute ans solvent in this caseIn this case, you consider that the solute is the component in less quantity and the solvent is the major component.
You know that a solution made of 15 g of oxygen and 5 g of helium. Then, helium is the solute and oxygen is the solvent.
Learn more about solvent and solute:
brainly.com/question/13133789
brainly.com/question/2614077
brainly.com/question/14129775
brainly.com/question/11985826
brainly.com/question/8620871
#SPJ1
what is a primary source
It takes 23 hours 56 minutes and 4 seconds for the earth to make one revolution (mean sidereal day). What is the angular speed of the earth?
angular speed = 7.29x10^-5 rad/s
Assume the earth is spherical. Relative to someone on the rotation axis, what is the linear speed of an object on the surface if the radius vector from the center of the earth to the object makes an angle of 49.0° with the axis of rotation. The radius of the earth is 6.37×103 km.
linear speed = 3.51 x 10^2 m/s
* What is the acceleration of the object on the surface of the earth in the previous problem?
Answer: See below
Explanation:
Part (a):
The angular speed of the Earth can be calculated as,
[tex]\omega &= \dfrac{{2\pi }}{T}\\ \omega &= \dfrac{{2\pi }}{{\left( {23 \times 3600} \right)\left( {56 \times 60} \right) + 4}}\\ \omega &= 7.29 \times {10^{ - 5}}\;{\rm{rad/s}}[/tex]
Part (b):
The linear velocity of the object can be calculated as,
[tex]v &= \omega r\sin \theta \\ v &= \left( {7.29 \times {{10}^{ - 5}}} \right)\left( {6.37 \times {{10}^6}} \right)\sin 47^\circ \\ v &= 339.62\;{\rm{m/s}}[/tex]
Part (c):
The acceleration of the object can be calculated as,
[tex]a &= \dfrac{{{v^2}}}{{r\sin \theta }}\\ a &= \dfrac{{{{339.62}^2}}}{{6.37 \times {{10}^6}\sin 47^\circ }}\\ a &= 0.024\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}[/tex]
Select the option no explanation needed
Answer:
c
Explanation:
the formula Torque = Force X Distance. While distance is measured in meters and force is measured in newton so torque is measured in newton ⋅ meter
a barber wants to setup a saloon in a measuring length of 3m by 3m. He has a simple wooden chairs,3 large mirror and one bulb. Using the knowledge of shadows and reflection, advice the barber on how to arrange a good saloon using the only item he has. Without adding more source of light, how can he enhance the lighting system in his saloon?
According to the information, it can be inferred that the best way to distribute the chairs and mirrors is to put the light system on a wall and put the 3 mirrors and chairs in front of the light as shown in the image.
How to distribute the objects to take advantage of the light from the bulb?To take advantage of the light from the bulb for the three chairs and the three mirrors, the objects must be placed in such a way that all three receive enough light to be able to carry out the work of cutting the hair.
So, the best option would be to put the bulb in the middle of a wall, and place a chair and mirror in front of the bulb. The other two chairs should be located one on each side of the centered chair and the mirrors in front of each chair.
Learn more about light in: https://brainly.com/question/26914812
#SPJ1
The figure below shows a man in a boat on a lake. The man's mass is 74 kg, and the boat's is 135 kg. The man and boat are initially at rest when the man throws a package of mass m = 15 kg horizontally to the right with a speed of vi = 5.0 m/s.
What is the velocity of the boat after the package is thrown? Neglect any resistance force from the water. (Give the magnitude in m/s, and select the correct direction from the options given.)
The velocity of the boat after the package is thrown is 0.36 m/s.
Final velocity of the boat
Apply the principle of conservation of linear momentum;
Pi = Pf
where;
Pi is initial momentumPf is final momentumv(74 + 135) = 15 x 5
v(209) = 75
v = 75/209
v = 0.36 m/s
Thus, the velocity of the boat after the package is thrown is 0.36 m/s.
Learn more about velocity here: https://brainly.com/question/6504879
#SPJ1
How long will it take a 50w motor to lift a 20 kg object 5 m?
Answer:
50+20=70
70÷5=14
Explanation:
50×20=1000
1000÷5=200
Answer:
Approximately [tex]20\; {\rm s}[/tex], assuming no energy loss and that [tex]g = 10\; {\rm N \cdot kg^{-1}}[/tex].
Explanation:
If the gravitational field strength is constantly [tex]g[/tex], lifting an object of mass [tex]m[/tex] by a height of [tex]\Delta h[/tex] would increase the gravitational potential energy ([tex]\text{GPE}[/tex]) of that object by [tex]m\, g\, \Delta h[/tex].
In this question, [tex]m = 20\; {\rm kg}[/tex] and [tex]\Delta h = 5\; {\rm m}[/tex]. Assume that [tex]g = 10\; {\rm N \cdot kg^{-1}}[/tex]. Hence, the [tex]\text{GPE}[/tex] that this object would eventual gain would be:
[tex]\begin{aligned}m\, g\, \Delta h &= 20\; {\rm kg} \times 10\; {\rm N \cdot kg^{-1}} \times 5\; {\rm m} \\ &= 1000\; {\rm N \cdot m} \\ &= 1000\; {\rm J}\end{aligned}[/tex].
Thus, this motor would need to do (at least) [tex]1000\; {\rm J}[/tex] of work to lift this object up by [tex]5\; {\rm m}[/tex]. The power rating of this motor, [tex]P = 50\; {\rm W} = 50\; {\rm J \cdot s^{-1}}[/tex], means that (assuming no energy loss) this motor could do [tex]50\; {\rm J}[/tex] of work every second.
The time it would take for this motor to do [tex]1000\; {\rm J}[/tex] of work under these assumptions would be:
[tex]\begin{aligned}t &= \frac{\text{work}}{\text{power}} \\ &= \frac{1000\; {\rm J}}{50\; {\rm J \cdot s^{-1}}} \\ &= 20\; {\rm s}\end{aligned}[/tex].
Particles q1 = -53.0 uc, q2 = +105 uc, and q3 = -88.0 uc are in a line. Particles qı and q2 are separated by 0.50 m and particles q2 and q3 are separated by 0.95 m. What is the net force on particle q3?
The net force on particle q3 is 112.11 N
What is electrostatic force?The electrostatic force F between two charged objects placed distance apart is directly proportional to the product of the magnitude of charges and inversely proportional to the square of the distance between them.
F = kq₁q₂/r²
where k = 9 x 10⁹ N.m²/C²
The Particles q1 = -53.0 uc, q2 = +105 uc, and q3 = -88.0 uc are in a line. Particles qı and q2 are separated by 0.50 m and particles q2 and q3 are separated by 0.95 m.
The net force F3 = F13 + F23
Substitute the values, we get the force F on q3 as
F3 = 9 x 10⁹x53.0 x 10⁻⁶x 88.0 x 10⁻⁶ / (0.5+0.95)² + 9 x 10⁹x105.0 x 10⁻⁶x 88.0 x 10⁻⁶ / (0.95)²
F3 = 112.11 N
Thus, the magnitude of the force on charge q3 is 112.11 N.
Learn more about electrostatic force.
brainly.com/question/9774180
#SPJ1
Identify the type of synthetic material used in each object. alloy ceramic polymer
The type of synthetic material used in each object include:
Tuba - AlloyPaper - PolymerPot - Ceramics.What is a Synthetic material?These are materials which are produced in the laboratory through different types of chemical processes.
Paper is made up of polymers such as Carboxylated styrene-butadiene latex etc.
Read more about Synthetic material here https://brainly.com/question/24357817
#SPJ1
Ben, a psychology student, decides to examine masking behaviors, now that more people are vaccinated. He goes to his local grocery store, finds a specific spot to sit, and counts the number of people he sees with masks or without masks across 2 weeks. Ben is most likely conducting a(n) ____________________ study.
Ben as a psychology student is most likely conducting a behavioral study.
What is psychology?
Psychology can simply be defined as the study of human mind, conscious and unconscious, thoughts and feelings.
In conclusion, Ben as a psychology student is most likely conducting a behavioral study.
Some few branches of psychology are:
Educational psychologyCognitive psychologyBehavioral psychologyCounseling psychologyForensic psychologyClinical psychologyLearn more about psychology:
https://brainly.com/question/12011520
#SPJ1
someone solvw this for me please
The velocity of the mass at time, t = 1 s, is determined as 20 m/s.
Magnitude of the force experienced by the body
The magnitude of the force experienced by the body is calculated as follows;
|F| = √(8² + 6²)
|F| = 10 N
Acceleration of the massFrom Newton's second law of motion;
F = ma
where;
m is massa is accelerationa = F/m
a = 10 /0.5
a = 20 m/s²
Velocity of the mass after 1 secondv = at
v = 20 x 1
v = 20 m/s
Learn more about velocity here: https://brainly.com/question/6504879
#SPJ1
A wire carries a 4.0-A current along the +x-axis through a magnetic field B= (5.0 i+7.0 j) T. If the wire experiences a force of 30 N as a result, how long is the wire?
Hello!
The equation for the magnetic force experienced by a wire is:
[tex]F_B = B \times iL[/tex]
F = Magnetic force on wire (30 N)
B = Magnetic field strength (5.0i + 7.0j)
i = Current in wire (4.0 A)
L = Length of wire (? m)
This is a CROSS-PRODUCT. We can rewrite this as:
[tex]F_B = BiLsin\theta[/tex]
Where 'θ' is the angle between the magnetic field and the current carrying wire.
Therefore, we would NOT count any field that is parallel to the wire. The field does have a component (5.0i) that is along the x-axis, so we would NOT count it because the wire is along this same axis.
This leaves the 'j' component, which is PERPENDICULAR to the wire. θ would then be 90°, and sin(90) = 1.
[tex]F_B = B\hat{j} iL[/tex]
Solving for the length:
[tex]L = \frac{F_B}{B\hat{j} i}\\\\L = \frac{30}{7(4)} = \boxed{1.07 m}[/tex]