a scuba diver makes a slow descent into the depths of the ocean. his vertical position with respect to a boat on the surface changes several times. he makes the first stop 8.0 m from the boat but has a problem with equalizing the pressure, so he ascends 3.0 m and then continues descending for another 10.0 m to the second stop. from there, he ascends 7.0 m and then descends for 14.0 m, ascends again for 6.0 m and descends again for 12.0 m, where he makes a stop, waiting for his buddy. assuming the positive direction up to the surface ( ĵ), express his net vertical displacement vector (in m) in terms of the unit vector ĵ. (express your answer in vector form.)

By using uniform motion, the high up the slope will it strike is 730.62 m.

We need to know about uniform motion to solve this problem. The uniform motion is an object's motion under acceleration. It should follow the rule

vt = vo + a . t

vt² = vo² + 2a . s

s = vo . t + 1/2 . a . t²

where vt is final velocity, vo is initial velocity, a is acceleration, t is time and s is displacement.

From the question above, we know that

θ = 70⁰

vi = 200 m/s

x = 300 m

Find the initial velocity in x and y axis

vx = vi cosθ = 68.40 m/s

vy = vi sinθ = 187.94 m/s

Find the time taken to reach 300 m

vx = x / t

68.4 = 300 / t

t = 4.39 second

Find the time taken to reach maximum height

vt = vo + a . t

0 = vy - g . t

vy = gt

187.94 = 9.8 . t

t = 19.18 second

The motion of projectile is raising to maximum height, hence

s = vo . t + 1/2 . a . t²

h = vy . t - 1/2 . g . t²

h = 187.94 . 4.39 - 1/2 . 9.8 . 4.39²

h = 730.62 m

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You walk in a given direction for 20 m during the first 5 seconds, your average speed is equal to 5m/s

Average speed is determined by dividing the total distance you travelled by the total time, whereas average velocity is determined by dividing your displacement (a vector pointing from your initial position to your end position) by the whole time.

The amount of something that happens or changes in a unit of time is expressed as a rate.

The equation for speed is that Divide the distance an object travels by the time it takes to cover that distance to determine its speed. A unit of distance is divided by a unit of time in the speed equation.

Then Average speed = total distance / total time

= 20 + 15 / 5 + 2

= 35/7

= 5 m/s

The average speed is calculated as 5m/s

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The minimum angle at which the box starts to slip is  20.30°, the acceleration once the box has begun to move is 1.10 m/s2 and final velocity of the box is 3.41 m/s^2.

Given:

Mass of the box m = 25.2 kg

Acceleration due to gravity g = 9.8 m/s^2

Coefficient of kinetic friction between the ramp and box  μk=0.25

Coefficient of static friction μs = 0.37

Part(A)

By inctreasing, parallel component of the weight will also increase but the force will decrease.

Let say θ be the angle of repose.

Now we know that

Ff= μs × mg × cosθ = mg × sinθ = Wp

Then we will get

θ = tan−1(μs)

θ = tan-1 (0.37) = 20.30 °

Part(B)

As the box starts sliding the frictional force becomes kinetic friction

The kinetic frictional force

F(k) = μ(k) x mg x cos(20.30)

= 0.25 × 25.2 × 9.8 × cos (20.30)

= 57.91 N

Now calculate the parallel component of the weight

W(p) = mg x sinθ

W(p) = 25.2 x 9.8 x cos (20.30)

= 85.68 N

Now calculate net force

F(net) = W(p) − F(k) = 85.68 − 57.91 = 27.77 N

Acceleration of the box

a = Fn/m = 27.77/25.2 = 1.10 m/s2

Part(C)

The box has moved a distance s = 5.3 m

The final speed of the box = v

Now

v = √ 2as

v = √ 2 x 1.10 x 5.3

v = 3.41 m/s^2

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The complete question is

A 25. 0 kg box of textbooks rests on a loading ramp that makes an angle α with the horizontal. The coefficient of kinetic friction is 0. 250, and the coefficient of static friction is 0. 350. Part A) As the angle θ is increased, find the minimum angle at which the box starts to slip. Express your answer using two significant figures. Part B) At this angle, find the acceleration once the box has begun to move. Express your answer using two significant figures. Part C) At this angle, how fast will the box be moving after it has slid a distance 5.3 m along the loading ramp? Express your answer using two significant figures.

The acceleration of Laura is 5.32 m/s² and that of Healen is 3.75 m/s².

Velocity is the directional speed of a moving item as an indication of its rate of change in position as seen from a specific frame of reference and measured by a specific time standard (e.g., 60 km/h northbound). The idea of velocity is crucial in kinematics, the part of classical mechanics that explains the motion of bodies.

A physical vector quantity called velocity requires both magnitude and direction to be defined. Speed is a coherent derived unit that expresses the scalar absolute value (magnitude) of velocity. Its quantity is expressed in SI units (metric system) of metres per second (m/s or ms1). For example, "5 meters per second" is a scalar while "5 meters per second east" is a vector.

Maximum speed of Laura is [tex]\Delta_{t1} = 2s[/tex]

Maximum speed of Healen is [tex]\Delta_{t2} = 3s[/tex]

Each runs at a constant acceleration for a given time interval, giving,

[tex]\Delta x_a = \frac{1}{2} a\Delta t^2[/tex]

This reaches final velocity

⇒ [tex]v = a\Delta t[/tex]

⇒ [tex]\Delta x_v = v(T - \Delta t)[/tex]

⇒ [tex]\Delta x_v =a\Delta t(T - \Delta t)[/tex]

Each sprinter's acceleration is calculated as follows:

Laura :-

⇒ [tex]\Delta t_1 = 2s[/tex]

⇒ [tex]a_1 = \frac{100m}{18.8s^2}[/tex]

⇒ [tex]a_1[/tex] = 5.32 m/s²

Healen :-

⇒ [tex]\Delta t_2 = 3s[/tex]

⇒ [tex]a_2 = \frac{100m}{26.7s^2}[/tex]

⇒ [tex]a_2[/tex] = 3.75 m/s²

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Full question

In a women's 100 m race, accelerating uniformly, Laura takes 2.00 s and Healan 3.00 s to attain their maximum speeds, which they each maintain for the rest of the race. They cross the finish line simultaneously, both setting a world record of 10.4 s.

A) What is the acceleration of each sprinter?

a) her speed is  26.43m/s

b)  Total distance traveled = 100 + 49.89

= 149.89m

c) Total time is 10.846 seconds

acceleration is the rate of change of the velocity of an object with respect to time.

From the question,

a) The car’s speed just after leaving the icy portion of the road is the first part

We have s = ut + 1/2at²

Here s = 100m, a = 1, u = 33.5 m/s

100 = 0* t + 1/2 * (-1) * t²

t = 7.07 seconds

After 7.07 seconds cars speed is given by v =u +at

u = 33.5m/s, a = -1

velocity = 33.5 + (-1) * 7.07 = 26.43m/s

So velocity of car on leaving icy surface = 26.43m/s

b) Time taken after icy surface

           0 = 26. 43 - 7 * t

            t = 3.776 seconds

 Distance traveled during this time

v² = u² + 2as

0 = (26.43)² + 2 * (-7) * S

s = 49.89 m

Total distance traveled = 100 + 49.89

= 149.89m

c) Total time taken = 3.776 + 7.07

Total time is 10.846 seconds

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The true statement for sinusoidal wave travelling  along a light weight string =

lambda₂<  lambda₁  and f₂ = f₁

λ₂ ≤ λ₂

The sine or sinusoidal wave may be a curve that describes a smooth repetitive oscillation. we will define the sine wave as “The wave form in which the amplitude is always proportional to sine of its displacement angle at every point of time”. All waves are often made by adding up sine waves

Then the waveform shape produced by our simple single loop generator is usually referred to as a Sine Wave as it is said to be sinusoidal in its shape. this sort of waveform is called a sine wave because it is based on the trigonometric sine function used in mathematics.

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In the Modified Block letter style, the date, complimentary close, and signature block are positioned approximately one-half inch to the right of center or at the right margin.

Following the proper format while writing business letters is crucial. There are specific methods that business letters have to be written.

The modified block letter style, which places one space between the body of the letter and the addresses of the sender and recipient, is one of the several letter kinds. In this form of letter, one space corresponds to around half an inch to the right of centre or at the right margin. Modified block letter formats are largely the same as full-block business letters.

Modified block format is a different extensively used format. The letter body, along with the sender and recipient's addresses, are left justified and single-spaced in this format. On the other hand, tab to the centre and start typing for the date and closure. Semi-Block. Semi-block is the last and least popular type of style.

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The statement "displacement tells the average direction of motion" regarding displacement is true.

Velocity is the directional speed of a moving item as an indication of its rate of change in position as seen from a specific frame of reference and measured by a specific time standard (e.g., 60 km/h northbound). The idea of velocity is crucial in kinematics, the part of classical mechanics that explains the motion of bodies.

A physical vector quantity called velocity requires both magnitude and direction to be defined. Speed is a coherent derived unit that expresses the scalar absolute value (magnitude) of velocity. Its quantity is expressed in SI units (metric system) of metres per second (m/s or ms1). For example, "5 meters per second" is a scalar while "5 meters per second east" is a vector.

Average velocity is calculated by taking the displacement vector from the start and end-point of an object’s path, and dividing its magnitude by the time interval. The average velocity always has the same direction as that displacement vector.

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Answer:

A hiker drops a heavy stone over a cliff and hear it strike the cliff base 2.8seconds after dropping it.

a)You throw a stone horizontally at a speed of 5.0 m/s from the top of a cliff that is 78.4 m high.

from above statement we got

height = 78.4 m

since the ball is thrown, so its vertical velocity would be zero

u = 0

taking g = 9.8m/s^2

now, using the equation of motion

h = ut + gt^2/2

now putting all the values in it

we got ,

78.4 = 9.8 * t^2/ 2

by solving we got,

t = 4 sec

b) now, since along the horizontal , no force acting and accelaration is zero so

R = ut , R is RANGE

R = 5 * 4

range =  20 m

c)  vertical components of the stone’s velocity just before it hits the ground = v sin θ =

horizontal   components of the stone’s velocity  just before it hits the ground = v cos θ

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The accelerations for each problem are:

1. 2.22m/[tex]s^{2}[/tex]

2. 7m/[tex]s^{2}[/tex]

3. 1.45m/[tex]s^{2}[/tex]

4. 20m/[tex]s^{2}[/tex]

The acceleration which is gained by the object because of gravitational force is called its acceleration due to gravity. Its SI unit is m/[tex]s^{2}[/tex]. Acceleration due to gravity is a vector, which means it has both magnitude and direction. The acceleration due to gravity at the surface of the Earth is represented by letter g. It has standard value defined as 9.80665 m/s2 (32.1740 ft/s2). However, actual acceleration of a body in free fall varies with location.

1. Initial velocity=0 km/h

Final velocity=24 km/h= 6.66m/s

Time=3 seconds

acceleration =[tex]\frac{6.66-0}{3}[/tex]=2.22m/[tex]s^{2}[/tex]

2. Initial velocity=0 km/h

Final velocity=35 m/s

Time=5 seconds

acceleration = [tex]\frac{35-0}{5}[/tex]=7m/[tex]s^{2}[/tex]

3. Initial velocity=20 km/h=5.55[tex]m/s^{2}[/tex]

Final velocity=60 km/h= 20m/[tex]s^{2}[/tex]

Time=10 seconds

acceleration= [tex]\frac{20-5.55}{10}[/tex]= 1.45m/[tex]s^{2}[/tex]

4. Initial velocity=50 m/s

Final velocity=150 m/s

Time=5 seconds

acceleration= [tex]\frac{150-50}{5}[/tex]= 20m/[tex]s^{2}[/tex]

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Answer: A. use a thicker piece of wire.

Explanation:

Answer:

Not really, because wearing a mask can lower your immune system and covid can be caught like any other virus body contact and body fluids. So since you can still get it through those ways then you're going to get it and be worse off than if you don't wear a mask.

you can test this by not wearing a mask and see how not bad it is catching covid over getting it while you wear a mask.

Explanation:

Answer:

Yes

Explanation:

Hypothesis- if masks are used to protect yourself from Covid-19 then the spread of the virus will decrease

You could test this by:

Getting a mask and using materials such as shampoo, soap, honey, glue,  or (safe) chemicals to see how much the masks absorbs the materials. By doing so you can show how the mask can help block certain materials from entering or leaving the mask area therefore slowing the spread of Covid.

Answer:The electrostatic force is directly related to the product of the charges and inversely related to the square of the separation distance.

Explanation:

Answer: solid state

Explanation:

The change from the liquid state to the solid state is called freezing. As the liquid cools, it loses thermal energy. As a result, its particles slow down and come closer together. Attractive forces begin to trap particles, and the crystals of a solid begin to form.

The average speed for the entire journey is 48 km/hr.

The average speed is the sum distance which is traveled by the object in a particular time interval, as the average speed is a scalar quantity and it is presented by the magnitude and has no direction.

here the first speed v₁ is 60 km/hr and the second speed v₂ is the 40 km/hr .So,  The formula we are referring to for calculating the average  speed

  S = 2v₁v₂/(v₁+v₂)

here,   v₁+v₂ =  60+40 =100

Now substituting the desired values  in the formula  

        =  2 x 60 x40/(100)

       =  4800/100

       = 48 km/hr

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The disadvantages of refractive telescopes include chromatic aberration and longer size.

This was the telescope developed by Newton in 1668.It is the simplest type of telescope which has a tube with lenses on both ends. The light enters through the lens on the farther end of telescope. The light is refracted to a point near the lens on the near end. It is then then further magnified when seen through the lens on the eyepiece.

Even though it was more reliable, it was really heavy and had a larger aperture and longer body. Since high quality lenses were costly to make, cheaper lenses were used mostly. So there was chromatic aberration.

Therefore, the disadvantages of refractive telescopes include chromatic aberration and longer size.

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The distance between you and the deer when you come to a stop is

s = d - 30 = 18 m.

The maximum speed you could have and still not hit the deer is

v = -5 + [tex]\sqrt{5}[/tex][tex]\sqrt{5 + 4d}[/tex]

  = 26m/s

You're driving down the highway late one night at 20m/s when a deer steps onto road d in front of you.

Your reaction time before stepping on the brakes is 0.50s and the maximum deceleration of your car is 10m/s2.

Given,

Speed = 20m/s

Time = 0.50 s

Distance = d

Deceleration = 10m/s2

D = R × T

D = Vi × Tr

D = (20 m/s) × (0.50 s)

D = 10 m

Dd = [ Vf^2 - Vi^2 ] / [ 2 × (-10 m/s^2) ]

Dd = [ (0.0 m/s)^2 - (20 m/s)^2 ] / (-20 m/s^2)

Dd = [ -400 m^2/s^2 ] / (-20 m/s^2)

Dd = 20 m

The total distance traveled is

Dt = D + Dd

Dt = (10 m) + (20 m)

Dt = 30 m

The distance between you and the deer when you come to a stop is

s = d - 30 = 18 m.

The maximum speed you could have and still not hit the deer is

v = -5 + [tex]\sqrt{5}[/tex][tex]\sqrt{5 + 4d}[/tex]

  = 26m/s

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The magnitude of force applied to the nails when they are located between point A and B is 37.5 N.

The magnitude of force applied to the nails when they are located between point B and C is 62.5N.

The force applied to the nails when they are located between point A and C is 29.41N

The moment exerted by the drill machine is: M =15 N⋅m

(a) The magnitude of force applied to the nails when they are located between point A and B.

Fa=M/AB

AB is distance between points A and B.

Plug in all the values in the above equation.

Fa=15 N⋅m/450mm

=15 N⋅m/0.45m

=37.5 N

Therefore, the magnitude of force applied to the nails when they are located between point A and B is 37.5 N.

(b)The magnitude of force applied to the nails when they are located between point B and C.

Fb=M/BC

BC is distance between points B and C.

Substitute all the values in the above equation.

Fb=15 N.m/240mm

=15 N.m/0.24m

= 62.5N

Thus, the magnitude of force applied to the nails when they are located between point B and C is 62.5N.

(c) The distance between points AC is,

AC=√(AB)2+(AC)2

Plug in all the values in the above equation.

AC=√(450mm)2 +(240mm)2

=510mm

=0.51m

The magnitude of force applied to the nails when they are located between point A and C.

Fc=M/AC

Substitute all the values in the above equation.

Fc=15 N⋅m/0.51m

=29.41 N

Thus, the force applied to the nails when they are located between point A and C is 29.41N

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Answer:

60 m/hStep-by-step

explanation:S = d/t

S= 360/60

S= 60

Ship A with a greater angle of projection will hit the target first.

The time of flight is the time a projectile takes to reach maximum height and return to the plane of projection. The time of flight is just double the maximum-height time.

Mathematically, time of flight is given as;

T = (2usinθ)/g

where;

The time of flight depends on initial velocity of the object and angle of projection.

When the initial velocity of both ships is the same and angle of projection varies, the difference in the time of flight will depend greatly on the angle of projection.

Thus, ship A with a greater angle of projection will hit the target first.

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Answer:

See below

Explanation:

d = 1/2 a t^2

1.226 = 1/2 a (.5)^2

a = 1.226/(1/2 * .5^2)

a = 9.808 m/s^2

A researcher tests acceleration due to gravity then the acceleration due to gravity measured by the researcher is 9.808 m/s².

In mechanics, acceleration refers to the speed at which an object's velocity varies over time. how many accelerations each vector has. An object's acceleration is determined by the direction of the net force exerted on it.

Due to the fact that it has both a magnitude and a direction, acceleration is a vector quantity. Velocity is a different vector property.

According to the question,

Time, t = 0.5 seconds

Distance, s = 1.226 meters

s = 1/2 a t²

1.226 = 1/2 a (0.5)²

a = 1.226 / (1/2 *0.5²)

a = 9.808 m/s²

So, the acceleration due to gravity is 9.808 m/s².

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The pressure when 32 newtons of force is applied to an area of 12.8 m² is 2.5 Pascals.

The force applied per unit area is defined as pressure.. Its S.I. unit is Pascal. 1 Pascal is equal to one Newton of force applied over an area of one meter squared. Its dimensional formula is [[tex]ML^{-1}[/tex][tex]T^{-2}[/tex]].

Pressure is directly proportional to the force applied and inversely proportional to the area over which the force is applied. And it follows the Pascal law.

Pressure = Force/Area

Given in the Question

Force = 32 Newton

Area = 12.8 m²

Put in the values, we get

Pressure = 32/12.8

Pressure = 2.5 Pascals

Therefore, the pressure when 32 newtons of force is applied to an area of 12.8 m² is 2.5 Pascals.

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Since an object's instantaneous velocity equals the derivative of its displacement at a certain point, we can also state that the instantaneous velocity at time t = 1 is around 2 meters per second.

The derivative of x with respect to t, or the upper limit of the average velocity as the elapsed time approaches 0, is the instantaneous velocity of an object:

v (t) equals d d t x (t). v (t) equals d d t x (t).

Instantaneous velocity is a vector having a dimension of length per time, similar to average velocity. The speed of an object at a specific time is its instantaneous speed. The instantaneous velocity is obtained by adding the direction to the speed.

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You have to double the period as well in order to keep it unchanged.

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed.

The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).

The formula for speed is as straightforward as dividing a distance by a time.

To calculate speed, divide the distance travelled (say, 3 metres) by the passing time (say, 3 seconds) (one metre per second).

So, the rate at which an object’s position changes in any direction can be defined as speed.

The speed formula is as follows: [Speed = Distance]

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Answer:

30 m/s

Explanation:

We can first list out the 3 kinematics equations:

[tex]v = u + at \\ {v}^{2} = {u}^{2} + 2as \\ s = ut + \frac{1}{2} a {t}^{2} [/tex]

Where:

v is the final velocity

u is the initial velocity

a is the acceleration

t is the time taken

s is the displacement

With all the 3 equations, we can now list the values needed for the first part of the question which is to find the acceleration for this first part.

Given:

v = 14 m/s

u = 6 m/s

t = 8s

We can use the first kinematics equation to solve for a. (v = u + at)

14 = 6 + a x 8

14 = 6 + 8a

8a = 14 - 6

8a = 8

a =

[tex]1 \frac{m}{ {s}^{2} } [/tex]

Now with this acceleration, we can find the final speed for the second part of the question by using the same kinematics equation. (v = u + at)

Given,

u = 14 m/s

t = 16 s

a =

[tex]1 \frac{m}{ {s}^{2} } [/tex]

v = 14 + (1)(16) = 14 + 16 = 30 m/s

The average speed with which the vehicle travels is equal to 56 Km/hr.

Velocity is measured as a vector quantity. There is a magnitude to it as well as a direction. The magnitude of velocity is measured by speed. The S.I. unit for this is the meter per second. Additionally, there are other units like km/h and km/s. Its dimensional equation is [LT-1].

The average speed of any vehicle is calculated over a given range of time. It is the total distance traveled by the vehicle in the given interval of time divided by the given time interval. It is a scaler quantity.

Average speed= Total Distance/ Time Taken

Given in the question

Distance = 140 km

Time of leaving Leeds = 8.00 am

Time of arriving Newcastle = 10.30 am

Time Taken = Time of arriving Newcastle - Time of leaving Leeds

                    = 10.30 - 8.00

                    =  2 hours and 30 minutes

So, the time taken is = 2.5 hr

Put in the values, we get

Average speed= Total Distance/ Time Taken

Average speed= 140/ 2.5 Km/Hr

Average speed= 56 Km/Hr

So, the average speed with which the vehicle travels is equal to 56 Km/hr.

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In a day, an electrical resistance heater uses 10 kW-h of electricity. In the same day, the heater delivers 9 kW-h of heat to the house in which it is located.

A measurement of an object's resistance to the flow of electrical current is called electrical resistance. Electrical conductance, which gauges how easily an electric current moves, is its reciprocal quantity. Mechanical friction and electrical resistance conceptually have some similarities. Electrical resistance is measured in ohms (), the SI unit of electrical resistance, whereas electrical conductance is measured in siemens (S), also known as the mho (), the SI unit of electrical conductance.

An object's resistance is significantly influenced by the material it is constructed of. Electrical insulators like rubber typically have very high resistance and low conductance, whereas electrical conductors like metals typically have very low resistance and high conductance. Resistivity or conductivity are used to measure this relationship.

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Since the cabinet must be mounted in a wet location, it must be mounted so there is at least 1/4 of airspace between the cabinet and the wall.

The area of the atmosphere that is under the authority of a nation above its territory, including its territorial waters, or, more broadly, any particular three-dimensional area of the atmosphere

It is not the same as aerospace, the umbrella term for the Earth's atmosphere and the proximity of outer space.

Wherever it is deemed necessary for air traffic control to exercise any sort of direct executive oversight over aircraft operating there, that area of the sky is known as controlled airspace.

A range of areas and zones, including those where flying operations are either completely prohibited or subject to restrictions, may be included in the further division of airspace.

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A device that regulates how much engine power flows to a machine's moving parts, frequently made of connected sets of wheels with teeth around the edges. Hence, option C is correct.

A gear is a spinning, circular machine element with teeth that can be cut, or in the case of a cogwheel or gearwheel, they can be inserted. These teeth, known as cogs, mesh with another toothed part to transmit (convert) torque and speed. The fundamental idea underlying how gears work is comparable to the fundamental idea behind how levers work.  Cog is another casual term for gear. A power source's speed, torque, and direction can all be altered by geared devices.

So, the exact definition of gear is that gears are wheels with teeth.

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Answer:

Gears are wheels with teeth