A boy walks 30m [E25°S] then 60m [E40°N]. Determine his net displacement.

The net force on the canoe rowed northward with an average force of 19.1 N is 4.7 N North if the wind is blowing directly south with an average force of 14.4 N.

Net force = Force due to rowing - Force due to wind

Net force = 19.1 - 14.4

Net force = 4.7 N

The direction is towards North because the force due to rowing is greater than the force due to wind.

If two force act in opposite directions, the resultant force is the difference of these two forces and the resultant direction is the direction in which the greater force is applied.  

Therefore, the net force on the canoe is 4.7 N North

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First, let's convert the distance of 4 lightyears to miles:

Now, let's find the time required:

Then, we need to convert from hours to years:

Therefore it will take approximately 69727 years.

The angle between the components x and y of a vector is given by:

once we know this we need to find in which quadrant the vector lies so we know how to calculate the correct direction.

Vector A lies in the fourth quadrant this means that we need to subtract theta to 360° in order to get the direction of the vector, then we have:

Therefore the direction of vector A is 343.61°

Vector B lies in the second quadrant, this means that we need to subtract theta (given by the first equation) to 180° in order to get the direction, then we have:

Therefore the direction of vector B is 105.26°

Let's find vector A+B:

Then we have that:

To find its magnitude we have to remember that the magnitude of any vector is given by:

Then for vector A+B we have:

Therefore the magnitude of vector A+B is 5.38 meters.

Vector A+B lies in the first quadrant, then its direction is given by the expression for theta, then we have:

Therefore the direction of vector A+B is 48.01°

Ball A with diameter d and ball B with diameter 2d are dropped from the same height. When the two balls have the same speed, the ratio of the drag force on ball A to the drag force on ball B will be F1 : F2 = 1 : 4

When objects travel through fluids (a gas or a liquid), they will undoubtedly encounter resistive forces called drag forces.

The drag force always acts in the opposite direction to fluid flow. If the body’s motion exists in the fluid-like air, it is called aerodynamic drag.

formula to calculate drag force is = F(d) = 1/2 * C * rho*A * [tex]v^{2}[/tex]

C = drag coefficient

A = area of object

rho = density in which object is moving

v = velocity of object

A = area of the object

F1 ( drag force on ball A ) = 1/2 * C * rho * area of ball A *  [tex]v^{2}[/tex]

F2 (drag force on ball A ) = 1/2 * C * rho * area of ball B *  [tex]v^{2}[/tex]

since , both the balls have same speed and falling in same environment hence , density and speeds are the same , the only difference is in area of both the balls

F1/F2 = area of ball A / area of ball B  =  4 * pi * [tex]r1^{2}[/tex] / 4 * pi * [tex]r2^{2}[/tex]

         =  [tex]r1^{2}[/tex]  /  [tex]r2^{2}[/tex]

         = [tex](\frac{d}{2} )^{2}[/tex]/ [tex](\frac{2d}{2}) ^{2}[/tex]

         = 1/4

F1 : F2 = 1 : 4

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The time read by the speedometer is, t = 4 s.

The strength of a gravitational field is denoted by gravitational acceleration (symbolized g). It is measured in meters per second (meters per second squared). At the earth's surface, 1 g equals 9.8 m/s2.

Therefore,

The time read by the speedometer is, t = 4 s.

Because the speedometer has a low precision, value approximation is possible.

For the speedometer showing the speed 20 m/s. The time is calculated as,

v = u + gt1

Here, u is the initial speed and g is the gravitational acceleration and its approximate value is, g ≈ 10 m/s²

Solving as,

10 = 0 + 10 t1

t1 = 1s

Thus, the time shown by the speedometer corresponding to speed of 10 m/s is 1 s.

For the speedometer showing the speed 20 m/s. The time is calculated as,

v = u + gt2

Solving as,

20 = 10 + 10 t2

t2 = 1s

Thus, the time shown by the speedometer corresponding to speed of 20 m/s is 1 s.

For the speedometer showing the speed 30 m/s. The time is calculated as,

v = u + gt3

Solving as,

30 = 20 + 10 t3

t3 = 1s

Thus, the time shown by the speedometer corresponding to speed of 30 m/s is 1 s.

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Option D

The law of conservation of charge states that the amount of charge in a system is constant

This means that as time changes, the amount of charge in a system does not change

By careful consideration of the options stated:

Each of options A to C either shows that charge is lost or gained

Only option D typifies the law of conservation of conservation of charges because charges are not lost or gained by the ballon so described.

ANSWER

The current through all three lamps in series is now 0.67 Amps. The current through each individual lamp is 0.67 Amps.

EXPLANATION

There are three lamps connected in series, each with a resistance of 3 Ω, resulting in a total resistance of 9 Ω.

By Ohm's law, if the voltage from the battery is 6 V, then the current through all three lamps - i.e. the total current in the circuit is,

And, since the three lamps are connected in series - which means there are no dividing paths, the current through each individual lamp is the same as the total current of the circuit, 0.67 Amps.

Hence, the current through all three lamps and through each individual lamp is 0.67 Amps, rounded to the nearest hundredth.

The work done by a force can be calculated with the formula below:

Where W is the work in J, F is the force in N and d is the distance in meters.

Since in this case, the attempt was unsuccessful, the car didn't move, so the distance is zero.

Therefore the work is zero, and the correct option is 5 (work is zero).

Answer:Laboratory thermometer

Explanation:

Mechanical energy (ME) = Potential energy(PE) + kinetic energy (KE)

PE = mgh

m= mass

g= gravity

h= height

KE= 1/2 m v^2

v= speed

Point B

ME = KE + PE

PE = 0 (height = 0 )

KE = 1/2 (m) v^2

180,000 = 1/2 (m) (20)^2

m = 180,000 / (1/2 (20)^2 )

m= 900 kg

Point A.

ME = 180,000 J = PEa + KE a

PEa = m g h = 900 (9.8) (20) = 176,400J

MEa = PEa + KEa

KEa = MEa - PEa = 180,000 - 176,400 J = 3,600 J

A) mass = 900 kg

B) 176,400 J

C) 3,600 J

ANSWER

EXPLANATION

We want to find the energy of the proton accelerated through the given potential.

To do this, apply the relationship between energy and potential:

where q = charge

V = potential

The charge of a proton is:

Therefore, we have that the energy of the proton is:

That is the answer.

Conductor that carries electrons:

From the pic we can conclude that the conductor is the wire, in this case it would be A.

Load that transforms energy:

From the pic, it is the bulb which transform the electric energy into light and heat, so it would be B

Insulation that prevents electrons from flowing:

It is the cable sheath, from the pic it is C

Area of low potential energy for electrons:

It is the negative part of the battery, from the pic it is E

Area of high potential energy for electrons:

It is the positive part of the battery, it is D

Given:

Atomic mass of carbon = 12 amu

Let's find how much mass of carbon would be needed to have an Avogadro's number (1 mole) of carbon atoms.

Given that the atomic mass of carbon is 12 atomic mass unit (amu), the amount of mass that would be need for 1 mole of carbon atom is = 12 g

ANSWER:

12 g

The true statement among the following is that the air is not affected by human movement. Hence, option C is correct.

Air relates to the atmosphere of the planet. Several gases and minute dust particles make up the air. Living organisms breathe and thrive in this pure gas. Its shape and volume are ill-defined. Considering that it is matter, it has mass and weight. Atmospheric pressure is generated by air weight. The space vacuum lacks air.

About 78% of the gas within air is nitrogen, 21% of the gas is oxygen, 0.9% of the gas is argon, 0.04% of the gas is co2, and very little other gas is present.

A typical amount of water vapor is around 1%.

Since respiration requires oxygen, animals must breathe it to survive. The lungs transfer back carbon dioxide back into the atmosphere when breathing, putting oxygen into the body.

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First, we need to find the spring constant

Force of gravity = force of tension from spring

mg = kx

(1x10^-3)(9.8) = k (3.2x10^-2)

k = .30625

Now we can look at the other situation

Since the spring was moved 0.01 meters, we can find the force

F = kx = (.01)(.30625) = .0030625 N

Now we can set the electric force equal to the force of the beads

kq^2/r^2 = .0030625 N

q = 292 microCoulombs

The initial kinetic energy of the car = 312.5 kJ

The initial volume of the car, v = 25 m/s

The mass of the car, m = 1000 kg

The initial kinetic energy is given by the formula

Substitute m = 1000 kg, and v = 25 m/s into the formula

The initial kinetic energy of the car = 312.5 kJ

We are asked to find the voltage drop at point A and B

Notice that point A and B have 3 resistors connected in parallel so the voltage across these 3 resistors will be the same.

First, we have to find the equivalent resistance of these 3 parallel resistors.

So, the resistance of the parallel resistors is 17.14

Now, we can simply use the voltage drop formula to find the voltage drop at point A and B

Where Vin is the input voltage that is 100 V

Therefore, there is a 14.63 V drop at point A and B

Let's put the given values into the formula below and get the result;

We know the numerical value of speed. We also know the mass. We can jump straight to the conclusion.

The Kinetic Energy is 25J.

If we want to accelerate an object, we must apply force on it, after applying Force some work has to be done in which energy should be transferred to the object. The energy is known as kinetic energy. The kinetic energy always depends on the mass and the velocity. It is denoted as K and the Si unit is Joules (J).

To calculate the Kinetic Energy,

           K= 1/2 mv^2

m = mass  

v = velocity

K = kinetic energy

In solving the above equation,

K = 1/2 x2 x 5^2

K = 5x5

K = 25

The Kinetic Energy is 25J.

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M = mass of the boy = 55kg

V = initial velocity of the boy = 12 m/s

m= mass of stationary skateboard = 15kg

v= velocity os stationary sketeboard= 0 m/s

V' = velocity of the boy on the skateboard after collision

Conservation of momentum:

MV + mv = (M + m) V'

Replacing:

55 kg * 12 m/s + 15 kg *0 = (55 kg+ 15 ) V'

Solve for V´'

660 = 70 V´'

660/70 = V'

V'= 9.42 m/s

Given:

The mass of the ball is

The speed of the ball is

Required: calculate the kinetic energy of the baseball

Explanation: to calculate the kinetic energy of a body we will use the formula as

first, we convert velocity from mi/h into m/s.

we know that

and

then the velocity is

now plugging all the values in the above formula, we get

Thus, the kinetic energy of the baseball is

The supplied puck is moving at a speed of v0x=+3.4m/s on an air hockey table at time t=0.

The direction of the movement of the body or the object is defined by its velocity. Most of the time, speed is a scalar quantity. In its purest form, velocity is a vector quantity. It measures how quickly a distance changes. It is the rate at which displacement is changing.

Any object traveling in a circular motion has a linear speed known as tangential velocity. On a turntable, a point in the center moves less distance in a full rotation than a point near the outside edge.

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Given:

h= 260m (height)

a = 9.8 m/s^2 (acceleration due to gravity )

Apply:

• a)

h = 1/2 a t^2

Replacing:

260 = 1/2 (9.8) t^2

260 / (1/2 * 9.8 ) = t^2

t = √[260 / (1/2 * 9.8 ) ]

t = 7.28 s

• b)

Apply.:

Vf = vi + at

Vf = finale velocity

Vi = initial velocity ( rest ) = 0 m/s

Vf = -9.8 (7.28 ) = -71.34 m/s

If the car does not brake, its mechanical energy will be conserved along all its trajectory.

Then, the sum of the kinetic energy (K) of the car and its gravitational potential energy (U) will be the same for any two points in the trajectory:

The kinetic energy of an object with mass m and speed v is:

The gravitational potential energy of an object with mass m at a height h above a reference level, is:

Where g is the acceleration of gravity.

In the beginning, the car has a height of 10m and a speed of 10m/s. In the end, the car reaches the gas station at a height 15m and a unknown speed v.

Then, the initial speed and height are known, as well as the final height. Use the equation for the conservation of mechanical energy to isolate v_2, the unknown final speed of the car:

Replace v_1=10m/s, h_1=10m, h_2=15m and g=9.8m/s^2 to find the speed of the car as it reaches the gas station:

Therefore, the car's speed as it coasts into the gas station on the other side of the valley will be approximately 1.4 meters per second.

Given,

The radius of the loop of the roller coaster, r=22.8 m

The forces that are acting on the roller coaster when it is at the top of the loop are the centripetal force directed upwards and the weight of the roller coaster including the passengers directed downwards.

For the passengers to stay in the seat, the centripetal force must be, at the least, equal to the weight of the passengers and the rollercoaster.

That is,

Where M is the combined mass of the rollercoaster and the passengers, v is the minimum speed of the roller coaster when it is at the top of the loop, and g is the acceleration due to gravity.

On simplifying the above equation,

On substituting the known values,

Thus the minimum speed that the roller coaster must have when it is at the top of the loop so that the passengers stay in contact with the seats is 14.95 m/s.

For a convex lens to form a virtua

The given statement 'Projections of a vector make up the components of that vector' is true. The direction of a vector

Answer:

Explanation:

Given:

m = 2.5 kg

V = 10 m/s

__________

Wk - ?

Wk = m·V² / 2

Wk = 2.5·10² / 2 = 125 J

Given,

The kinetic energy of the car, E=2400 J

The speed of the car, v=20 m/s

Kinetic energy is the energy that is possessed by an object due to its motion.

It is given by,

Where m is the mass of the car.

On substituting the known values in the above equation,

Thus the mass of the car is 12 kg