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Alecsey [184]
3 years ago
10

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of

18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds? Assume that right of center is a positive distance and left of center is a negative distance.
a) d=9cos(pi/4 t)
b) d=9cos(pi/2 t)
c) d=18cos(pi/4 t)
d) d=18cos(pi/2 t)
Physics
2 answers:
sdas [7]3 years ago
8 0

Answer:

The correct answer is b,  x = 9 cos (pi / 2 t)

Explanation:

The equation that describes a simple pendulum is

             θ  = θ₀  cos (wt + φ)

The angle is measured is radians

            θ = x / L

We replace

           d / L = x₀ / L cos (wt + φ)

            x₀ = 9 in

         

We replace

             d = 9 cos (wt + φ)

Angular velocity is related to frequency and period.

           w = 2π f = 2π / T

The period is the time of a complete oscillation T = 4 s

           w =2π / 4

           w = π / 2

Let's replace

             x = 9 cos (π/2 t + φ)

As the system is released from the root x = x₀ for t = 0 s

              x₀ = x₀ cos φ

             Cos φ = 1

             φ = 0°

The final equation is

             x = 9 cos (pi / 2 t)

The correct answer is b

N76 [4]3 years ago
6 0

Answer:

b) d=9cos(pi/2 t)

Explanation:

This is a cosine function in the such as: y = a cos bt...

a = (maximum distance - minimum distance)/2:

a = (max - min)/2

maximum distance = 18 inches minimum distance = 0

a = (18 - 0)/2 = 18/2 = 9

That is a = 9

To solve for b, similar to the period:

The period in radians:

P = 2pi/b, which is the amount of time it takes to revolve one full cycle...

multiply that time by time from minimum to maximum, 2 to give the period as 2 × 2 = 4.

Thus to find b..

4 = 2pi/b

4b = 2pi/b × b

4b = 2pi

or

b = pi/2

Also

a = 9

b = pi/2

So our cosine function is:

d = 9cos((pi/2)t)

Hence the equation that models d

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Dimas [21]

Answer:

49.63 degree

Explanation:

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angle of incidence = 59 degree

Let r be the angle of refraction

The refractive index of glass, ng = 3/2

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refarctive index of glass with respect to water = ng / nw = 3 /2 ÷ 4 /3 = 9 / 8

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9 / 8 = Sin 59 / Sin r

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3 years ago
the idling engines of a landing turbojet produce forward thrust when operating in a normal manner, but they can produce reverse
Finger [1]

Forward thrust has positive values and reverse thrust has negative values.

Thrust is a sudden push or pull in a certain direction.

a)

Flight speed u = 150 km/h

1 km/h = \frac{1}{3.6} km/s

therefore, 150 km/h =  41.67 km / s

The thrust force represents the horizontal or x-component of momentum equation:

T = m_{exhaust} * U_{exhaust} - U_{flight}

T = 50 * (150 - 41.67)

T = 5416.67 N

Therefore, the value of forward thrust is 5416.67 N.

b)

Now the exhaust velocity is now vertical due to reverse thrust application, then it has a zero horizontal component,

thus thrust equation is:

T = m_{exhaust} * U_{exhaust} - U_{flight}

T = 50 * (0 - 41.67)

T = -2083.5 N

Therefore, the thrust force T is -2083.5 N in the reverse direction.

c)

Now the exhaust velocity and flight velocity is zero, then it has a zero horizontal component, thus thrust is also zero becauseU_{exhaust} = U_{flight} = 0\\

T = 0

Therefore, there is no difference in two velocities in x direction.

The given question is incomplete, the complete question is,

"The idling engines of a landing turbojet produce forward thrust when operating in a normal manner, but they can produce reverse thrust if the jet is properly deflected. Suppose that while the aircraft rolls down the runway at 150 km/h the idling engine consumes air at 50 kg/s and produces an exhaust velocity of 150 m/s.

a. What is the forward thrust of this engine?

b. What are the magnitude and direction (i.e., forward or reverse) if the exhaust is deflected 90 degree without affecting the mass flow?

c. What are the magnitude and direction of the thrust (forward or reverse) after the plane has come to a stop, with 90 degree exhaust deflection and an airflow of 40 kg/s?"

To know more about thrust,

brainly.com/question/14552836

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3 0
1 year ago
If you had 8 balls and 7 of them were a certain weight, and 1 of them was heavier, how could you find the heaviest ball. All the
dybincka [34]

Answer:

There are two method of comparing the balls 1) using a balance  2) by  only 2 weighings.

Explanation:

There are two method of comparing the balls 1) using a balance  2) by  only 2 weighings.

Make the following groups - --- (1,2,3),(4,5,6),(7,8)

Step 1. compare the Weigh (1,2,3) and (4,5,6)

there are 2 possible outcomes:

1---both the group are of same weight. and named as (Case A)

2--- one of the group is heavier than other and named as  (Case B)

Step 2. Let examine both case

In Case A --in this case, now compare the weight of 7th and 8th ball. By this you have recognize the heavier ball by 2 weighing method.

In Case B -- considered the heaviest group (assume group (1,2,3) is heavy), from this group take randomly two ball and compare the their weight. out of these two ball, one  is heavy else the third ball is.

7 0
3 years ago
Car A has a mass of 1,200 kg and is traveling at a rate of 22 km/hr. It collides with car B. Car B has a mass of 1,900 kg and is
anastassius [24]

The car A has a mass of 1200 kg.

The car B has the mass of 1900 kg.

It is given that velocity of car  A is given as 22 Km/hr

The car B has the velocity of 25 Km/hr.

Let the mass of two bodies are denoted as  m_{1} \ and\ m_{2}

Let the velocity of cars A and B are denoted as v_{1} \ and\ v_{2}

The momentum before collision is-

                                                  p_{i} =m_{1} v_{1} +m_{2} v_{2}

[Here p stand for momentum.]

We are asked to calculate the final momentum of the system after collision.

The answer of the question is based law of conservation of  linear momentum.

As per law of conservation of linear momentum the sum total linear momentum for an isolated system is always constant.Hence irrespective of the type of collision[elastic and inelastic],the momentum of the system is always constant which is a universal truth.

Let after the collision the velocity of A and B are v'_{1} \ and\ v'_{2}

Hence the final momentum of the system is-

                                                        p_{f} = m_{1} v'_{1} +m_{2} v'_{2}

As per the law of conservation of linear momentum, the initial and final momentum must be equal i.e      

                              p_{i} =p_{f}

                               m_{1} v_{1} +m_{2}v_{2} =m_{1} v'_{1} +m_{2} v'_{2}

Hence the option A  is right.

7 0
3 years ago
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