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If a hydraulic catapult propels the car to the top of the ride, at a height of 405 ft. If the car and occupants weigh 1188 lb, then the potential energy of the loaded car at the top would be 652542.68 Joules.

Mechanical energy is the combination of all the energy in motion represented by total kinetic energy and the total stored energy in the system which is represented by total potential energy.

As given in the problem, for the roller coaster, a hydraulic catapult propels the car to the top of the ride, at a height of 405 ft. If the car and occupants weigh 1188 lb,

1 lb = 0.4536 Kg

1188 lb = 1188× 0.4536 Kg

           =538.87 Kilograms

1 ft = 0.3048 meters

405 ft = 405×0.3048 meters

          =123.44 meters

The potential energy of the loaded car at the top = mgh

                                                                                   =538.87×9.81×123.44

                                                                                   =652542.68 Joules

Thus, the potential energy of the loaded car would be 652542.68 Joules.

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The average force exerted by seatbelts on the passenger is 1493.3N.

initial velocity of the car, u = 96km/h

time taken by the car, s = 5.0 sec

final velocity of the after coming to rest, v = 0

mass of the passenger, m = 56 kg

to find out the acceleration of the car we use equation of motion

v = u+ at

0 = 96km/h + ax 5s

a = - 96 x 18/5x5

a = -26.6m/s²

The deceleration of the car is 26.6 m/s²

The force exerted on the passenger by the backward action of the car is calculated as

F = ma

where

m is mass

a is acceleration

F = 56 x 26.6

F = 1493.3 N

Therefore, the average force exerted by seatbelts on the passenger is 1493.3N.

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Answer:

[tex]{ \tt{X( \omega) = x(t)}}[/tex]

The age of the sample will be 11460 years.

The half-life of C-14 = 5730 years.

The half- life time is the time taken by the object to attain its position till the half of its initial value.

i.e after 5730 years only half of the C-14 carbon will exists.

To retain one-fourth of the sample, another cycle of 5730 years is required.

This means 2 half-lives should have passed to retain one-fourth of the sample.

so to calculate it's age

[tex]\frac{t}{\frac{t}{\frac{1}{2} } }[/tex] = 2

where t = the age of the sample

with t(1/2) = the half-life time of the sample = 5470 years

2 = the number of half- lives passed

therefore

[tex]\frac{t}{5730}[/tex] = 2

t = 2*5730 = 11460 years

When only one-fourth of the sample will remain, the age of the sample will be 11460 years

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(a) The cheetah's average acceleration during the short sprint is 5.67 m/s²

(b) The displacement of the cheetah after the given time is 94.42 m.

The average acceleration of the cheetah is calculated as follows;

v² = u² + 2as

where;

u is initial velocity = 78 km/h = 21.67 m/s

v is the final velocity = 114 km/h = 31.67 m/s

31.67² = 21.67² + 2(47)a

31.67² = 21.67² + (94)a

94a = (31.67² - 21.67²)

a = (31.67² - 21.67²)/94

a = 5.67 m/s²

s = ut + ¹/₂at²

s = (21.67 x 3.1)  +  ¹/₂(5.67)(3.1²)

s = 94.42 m

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The early phases of undertaking an epidemiological, clinical, or lab study include calculating the sample size. There are ethical and methodological guidelines that should be followed when creating a scientific publication.

When it comes to making clinical judgments, two studies that used the same approach and produced equal results but had different sample sizes could provide the researcher with different information. Therefore, contrary to popular belief, samples should not be too tiny or too large in the perfect world. The primary effects of the sample size on study interpretation will be covered in this paper using clinical terminology. Although it can appear at first glance that methodological difficulties are the most important thing, particularly to clinicians.

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The conservation of mass and energy just means that they can't be destroyed, only changed into other forms. For example, when we burn something, the matter isn't going away. It is just changing into heat and light energy. After any chemical reaction, the amount of matter and energy will stay the same.

Answer:

Fire is in plasma physical state. It contains both gaseous and moist fluidy substances.

[tex].[/tex]

Answer:

Both gas state and liquid state or vapor (plasma overall)

Adding base ions to a solution will make the solution more basic.

When base ions are added it indicates adding OH⁻ ions, which will increase the pH of the solution and hence free H⁺⁺ ions will be decreased which leads to the increase in basicity of the solution.

pH is a logarithmic measure of the concentration of hydrogen ions in an aqueous solution.

Therefore if the base ions are added to the solution, pH of the solution will increase and hence it will become more basic.

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The average velocity of the electron over the entire time interval is 1.182 x 10⁷ m/s.

The average speed of the electron over the entire time interval is  6.454 x 10⁷ m/s.

The average velocity of an object is the change in the displacement of the object with time.

average velocity = total displacement / total time of motion

average velocity = (final position - initial position)/total time

average velocity = (2.39 m - 1.65)/(2.89 x 10⁻⁸  +  3.37 x 10⁻⁸)

average velocity = 1.182 x 10⁷ m/s

The average speed of an object is ratio of total distance to total time of motion of the object.

average speed =  (2.39 m + 1.65 m)/(2.89 x 10⁻⁸  +  3.37 x 10⁻⁸)

average speed = 6.454 x 10⁷ m/s

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One must drive at a speed of 62.5 miles per hour to reach the theatre at time.

Time movie starts in: 40 minutes

Time taken to drive to friend's house: 10 minutes

Time taken to drive to the theatre from friend's house:  15 minutes

Speed = 40 miles per hour

Using the formula to find the distance:

Speed = Distance/Time

40 = Distance/(15/60)

40*0.25 = Distance

10 miles is the distance from the friend's house to the theatre

Now, time taken by friends while playing games = 20 minutes

Time remaining = 40 - 10 - 20 = 10 minutes

The distance required to be covered in 10 minutes is 10 miles

Therefore, using the formula we get:

Speed = 10/(10/60)

Speed = 62.5 miles per hour

Hence, one should drive at a speed of 62.5 miles per hour to reach the theatre on time

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The distance between the hands is obtained as 13 ft.

Let us commence by restating the definition of distance as the difference between two points. Now from the image we can see the geometry of the problem. The minute hand is clearly much longer than the hour hand we can not solve this problem if we do not involve the Pythagoras theorem seeing that a right angled triangle has to be formed in this case here.

Length of the minute hand =  17.0 ft

Length of the hour hand = 11.0 ft

Using the Pythagoras theorem;

c^2 = a^2 + b^2

b^2 = c^2 - a^2

b = √c^2 - a^2

b = √(17.0)^2 - (11)^2

b = 13 ft

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Explanation:

Answer:

B

Explanation:

The ice begins to melt which requires it absorb heat from the water...the water gets cooler and the ice gets smaller

Answer:

yes

Explanation:

Answer:

-68.6m/s

Explanation:

after 1 second its velocity is -9.8 m/s. after 2 seconds its velocity is -19.6 m/s. after 3 seconds its velocity is -29.4 m/s.

so 7 multiplied by the velocity for 1 second will give you the answer.

Answer: Airbag

Explanation:

Provides safety to passengers during a collision.

The vertical distance with which the ball clears the crossbar is given by x= 1.34m

We are given in the question that the distance between the kicking point of football and the goal is 54m (59.0544 yd), Height of crossbar is 3.05m, Speed of the ball when it leaves the ground is 26m/s at an angle of 32.6° from horizontal and the acceleration due to gravity is 9.8 m/s².

The ball will follow projectile motion when kicked and the equation for finding time in a projectile motion is given by:

t = d/vcosθ

=> t = 54/(26×cos32.6°)

=> t = 2.5 s

Now newton's second equation of motion for finding distance in y direction is given by:

S= ut - 1/2(at²)

S=(26sin32.6°)2.5 - 1/2(9.8×2.5²)

S= 4.39m

Therefore, the vertical distance with which the ball clears the crossbar is given by x= 4.39 - 3.05 = 1.34m

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It takes less effort to lift a piano with a pulley. If the piano is lifted 3 meters, then the distance traveled by the load is 3 m.

Output force is the force exerted on an object by a simple machine.

If the output force is greater than the input force, the mechanical advantage is greater than 1.

The mechanical advantage ratio is output force divided by input force. The larger the mechanical advantage, the easier it is to do work.

Mathematically, the output force of a simple machine is given as;

output force = load x distance moved by load

Thus, it takes less effort to lift a piano with a pulley. If the piano is lifted 3 meters, then the distance traveled by the load is 3 m.

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Answer:

Explanation:

The correct option will be the option (d) that is copyright.

The legal right given to a creator for a work to earn profit from it is known as copyright. That works can be about books, music, painting, sculptures, and films, any database programs, advertisements, new technology, maps etc. if any person doesn’t the follow the protocols of this copyright rule then he/she will be punished.  For that he/she might have to pay some money for stealing the creator’s work.

So, the correct option will be the copyright.

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The magnitude of the force on the 89 kg person who is decelerating at 30 m / s² is 272.44 N

According to Newton's second law of motion,

F = m a

m = W / g

F = Force

m = Mass

a = Acceleration

W = Weight

g = acceleration due to gravity

a = 30 m / s²

W = 89 kg  

F = 89 * 30 / 9.8

F = 272.44 N

According to Newton's second law of motion, Acceleration of an object is dependent upon the mass of the object and the net force acting on it.

Therefore, the magnitude of the force on the 89 kg person who is decelerating at 30 m / s² is 272.44 N

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The charge is obtained as 5.35 * 10^-9 C.

The electric filed is defined as the region in space where the influence of a charge is felt. In this case, we know that the magnitude of the electric charge has been given to be 4.70 N/C and the distance is 3.20 m.

Let us recall that;

E = Kq/r^2

K = electric field constant

q = magnitude of charge

r = distance of separation

E = Kq/r^2

Er^2 = Kq

q = Er^2/K

q =  4.70 N/C * (3.20 m)^2/9.0 * 10^9

q = 5.35 * 10^-9 C

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The time taken for the ball to hit the ground is 1.77 s

From the questionn give above, the following data were obtained:

The time taken for the ball to fall to the ground can be obtained as follow:

h = ½gt²

15.3 = ½ × 9.8 × t²

15.3 = 4.9 × t²

Divide both side by 4.9

t² = 15.3 / 4.9

Take the square root of both side

t = √(15.3 / 4.9)

t = 1.77 s

Thus, we can conclude that: it will take the ball 1.77 s to fall to the ground.

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Answer:

Explanation:

The correct answer will be that the internet in north korea, Saudi Arabia and  china is controlled by the government.

As in these countries according to the constitution of these countries there is a very much restriction on the civilians even for the internet usage. So the internet usage is controlled by the government in these countries.

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The correct answer 12.611 mph.

Cyclist traveling in a northwest direction at a speed of 16 mph. (Directed 45 degrees from the North)

Cycling speed is therefore 16 sin (45 o) in the direction of the north and 16 cos (45)  in the direction of the west

Let's assume that this is located on a cartesian plane. Let the positive Y-axis be north and the positive X-axis be east.

Speed = [tex]V_c[/tex] = (-16/√2 i + 16/√2 j) mph

In relation to a cyclist, the wind speed is = [tex]V_{cw[/tex] = 17 i mph

Let, V_w thus,

[tex]V_{cw = V_w - V_c[/tex]

[tex]V_w = V_{cw + V_c[/tex]

[tex]V_w[/tex] = 17i +  (-16/√2 i + 16/√2 j)

[tex]V_w[/tex] = (17 - 16/√2) i + 16/√2 j

[tex]V_w[/tex] = 5.6 i + 11.3 j

| [tex]V_w[/tex]| = 12.611

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The volume of the rock, given the data is 14 mL (Option A)

From the question given above, the following data were obtained:

The volume of the rock can be obtained by calculating the displacement of the water when the rock was added. this can be obtained as follow:

Displacement of water = (Volume of water + rock) - (volume of water)

Displacement of water = 34 - 20

Displacement of water = 14 mL

Thus, the volume of the rock is 14 mL

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Complete question:

See attached photo

The color change would be an example of qualitative observation.

The approach of conducting research known as qualitative observation uses subjective methodologies to collect information or data. Although qualitative observation takes a lot longer than quantitative observation because the goal is to compare quality differences, the research is vast and much more individualized.

The five main senses—sight, smell, touch, taste, and hearing—and how they function are the topics of qualitative observation. This involves attributes rather than measures or numbers.

Hence, recording a color change would be an example of a qualitative observation.

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The applied force needed to lift both buckets up is 71 N.

The net force applied on the buckets is calculated as follows;

F(net) = F(T) + (-Fg)

where;

Substitute the given parameters and solve for the net force on the bucket.

F(net) = 60 N - (5 x 9.8)

F(net) = 60 N - 49 N

F(net) = 11 N

The force needed to lift the bucket = F(net) + F(T)

F(app) = 11 N + 60 N

F(app) = 71 N

Thus, the applied force needed to lift both buckets up is 71 N.

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Answer:

S = Vx t = 900 t

t = 150 / 900 = 1/6 sec  

If the bullet is fired horizontally it will travel 900 m in .167 sec

H = 1/2 g t^2 = 1/2 * 10 * (1/6)^2 = .139 m      distance bullet will fall

A) the maximum weight of the air-conditioning unit allowed is 557.7 N. and B) the work done by force F on the object that undergoes displacement is 456.75 J.

Given in the question,

The angle of the Slope = 39 Degrees

Max Weight perpendicular of the roof allowed = 435 N

Distance of roof = 1.3 meters

Let us assume the force of the weight of air-conditioning unit be F.

Now as the roof is at the slope of 39 degrees, The weight perpendicular to the roof tile will be the cos component of the force F.

Max perpendicular Weight = F×(cos(Ф)),

Put in the values, we get

F × Cos(39) = 435

F = 435/Cos(39)

F = 435/0.78   [ Value of cos39 = 0.78 ]

F = 557.7 N

a) So, the maximum weight of the air-conditioning unit allowed is 557.7 N.

b) If the unit sides down the roof, the vertical distance traveled by the unit will be the sin component of the length traveled by it along the roof.

Vertical Displacement = (Length Along Roof)× Sin(39)

Force vertically Downward =  F = 557.7 N

Using Formula, W= F.s, Put in the value, we get

W = F × (Length Along Roof)× Sin(39)

W = 557.7 × 1.3 × 0.63

W = 456.75 J

So, A) the maximum weight of the air-conditioning unit allowed is 557.7 N. and B) the work done by force F on the object that undergoes displacement is 456.75 J.

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