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andrey2020 [161]
3 years ago
13

A spiral staircase winds up to the top of a tower in an old castle. To measure the height of the tower, a rope is attached to th

e top of the tower and hung down the center of the staircase. However, nothing is available with which to measure the length of the rope. Therefore, at the bottom of the rope a small object is attached so as to form a simple pendulum that just clears the floor. The period of the pendulum is measured to be 5.94 s. What is the height of the tower?
Physics
1 answer:
boyakko [2]3 years ago
8 0

Answer:

8.76762 m

Explanation:

T = Time period = 5.94 seconds

g = Acceleration due to gravity = 9.81 m/s²

L = Length of pendulum = Height of tower

Time period is given by

T=2\pi \sqrt{\dfrac{L}{g}}\\\Rightarrow T^2=4\pi^2\dfrac{L}{g}\\\Rightarrow L=\dfrac{T^2g}{4\pi^2}\\\Rightarrow L=\dfrac{5.94^2\times 9.81}{4\pi^2}\\\Rightarrow L=8.76762\ m

The height of the tower is 8.76762 m

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When magnesium fluoride reacts with iodine, the products are fluorine and magnesium iodide. What would the equation be?
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Answer:

Explanation:

Every chemical reaction can be represented by simple chemical equations that shows how compounds are combining to give some products.

Such reactions are usually made up of:

     Reactants on the left hand side

     Products on the right hand side

            Reactants  →  Products

In this given problem;

            Reactants are :   Magnesium fluoride  = MgF₂

                                             Iodine in form of Iodide   = I₂

           Product : Magnesium iodide  = MgI₂

             

               MgF₂   +     I₂    →       MgI₂   +   F₂

   

                             

   

7 0
3 years ago
If a true heading of 135° results in a ground track of 130° and a true airspeed of 135 knots results in a groundspeed of 140 kno
vladimir2022 [97]

Answer:

245.1° and 13 knots

Explanation:

The given parameters are;

The true heading = 135°

The resultant ground track = 130°

The true airspeed = 135 knots

The ground speed = 140 knots

Given that the true airspeed the ground speed and the wind direction and magnitude form a triangle, we have;

From cosine rule, we have;

a² = b² + c² - 2×b×c×cos(A)

Where

a = The magnitude of the wind speed in knot

b = The true airspeed = 135 knots

c = The ground speed = 140 knots

A = The angle in between the true heading and the resultant ground track heading = 5°

Which gives;

a² = 135² + 140² - 2×135×140×cos(5 degrees) = 168.84 knots²

a = √168.84 = 12.9934 ≈ 13 knots

We have;

135 × sin(135 degrees) - 140× sin(130 degrees) = -11.7868

135 × cos(135 degrees) - 140× cos(130 degrees) = -5.469

Tan(θ) = -11.8/-5.5 = 2.155

θ = tan⁻¹(2.155) = 65.108°

Given that the wind is moving in opposite direction (slowing down the airplane, we add 180°, to get

Therefore, the angle direction = 180 + 65.108 = 245.1

Therefore, we have;

245.1° and 13 knots

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The _____ rip and grind food into small chunks.
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Find the position of the center of mass of the system of the sun and Jupiter? (Since Jupiter is more massive than the rest of th
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Answer:

r_{cm} = 0.074 m from the position of the center of the Sun

Explanation:

As we know that mass of Sun and Jupiter is given as

M_s = 1.98 \times 10^{30} kg

M_j = 1.89 \times 10^{27} kg

distance between Sun and Jupiter is given as

r = 7.78 \times 10^{11} m

now let the position of Sun is origin and position of Jupiter is given at the position same as the distance between them

so we will have

r_{cm} = \frac{M_s r_1 + M_j r_2}{M_s + M_j}

r_{cm} = \frac{1.98 \times 10^{30} (0) + (1.89 \times 10^{27})(7.78 \times 10^{11})}{1.98 \times 10^{30} + 1.89 \times 10^{27}}

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