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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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Assume that the speed of light in a vacuum has the hypothetical value of 18.0 m/s. A car is moving at a constant speed of 14.0 m
denis23 [38]

Answer:

4.245s

Explanation:

Given that,

Hypothetical value of speed of light in a vacuum is 18 m/s

Speed of the car, 14 m/s

Time given is 6.76 s, and we're asked to find the observed time, T

The relationship between the two times can be given as

T = t / √[1 - (v²/c²)]

The missing variable were looking for is t, and we can find it if we rearrange the formula and make t the subject

t = T / √[1 - (v²/c²)]

And now, we substitute the values and insert into the equation

t = 6.76 * √[1 - (14²/18²)]

t = 6.76 * √[1 - (196/324)]

t = 6.76 * √(1 - 0.605)

t = 6.76 * √0.395

t = 6.76 * 0.628

t = 4.245 s

Therefore, the time the driver measures for the trip is 4.245s

8 0
3 years ago
n deep space, sphere A of mass 47 kg is located at the origin of an x axis and sphere B of mass 110 kg is located on the axis at
Volgvan

Answer:

a)-1.014x 10^{-7J

b)3.296 x  10^{-7J

Explanation:

For Sphere A:

mass 'Ma'= 47kg

xa= 0

For sphere B:

mass 'Mb'= 110kg

xb=3.4m

a)the gravitational potential energy is given by

U_{i = -GMaMb/ d

U_{i= - 6.67 x 10^{-11} x 47 x 110/ 3.4 => -1.014x 10^{-7J

b) at d= 0.8m (3.4-2.6) and U_{i=-1.014x 10^{-7J

The sum of potential and kinetic energies must be conserved as the energy is conserved.

K_{i + U_{i= K_{f + U_{f

As sphere starts from rest and sphere A is fixed at its place, therefore K_{i is zero

U_{i= K_{f + U_{f

The final potential energy is

U_{f= - GMaMb/d

Solving for 'K_{f '

K_{f = U_{i + GMaMb/d => -1.014x 10^{-7 + 6.67 x 10^{-11} x 47 x 110/ 0.8

K_{f = 3.296 x  10^{-7J

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Assume a nation's nominal GDP is $5 trillion with an inflation rate of 5%. find its real GDP. PLEASE HELPPPPPPPPPPPPPPPPPPPPP
erastova [34]

Answer:

I don't know

Explanation:

But if you need help or reference America's GDP is 19.8 trillion dollars it spends over 2 to 3 percent of its budget on the military and the military's budget is 250 billion dollars

PS: sorry if the reference didn't help and if this doesn't help write dow the problem and download PHOTO MATH take a picture and buala and if you need to show your work just click on the button that says brake down problem and it'll show you and teach you the steps

7 0
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