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Karolina [17]
3 years ago
14

A man 2 m tall walks horizontally at a constant rate of 1 m/s toward the base of a tower 23 m tall. When the man is 10 m from th

e tower, at what rate is the angle of elevation changing if that angle is measured from the horizontal to the line joining the top of the man's head to the top of the tower? (Round your answer to three decimal places.)

Physics
1 answer:
Evgen [1.6K]3 years ago
8 0

Answer:

\dfrac{d\theta}{dt}=0.038\ rad/s

Explanation:

Given that

\dfrac{dx}{dt}= -1\ m/s

From the diagram

tan\theta=\dfrac{21}{x}

By differentiating with time t

sec^2\theta \dfrac{d\theta}{dt}=-\dfrac{21}{x^2}\dfrac{dx}{dt}

When x= 10 m

tan\theta=\dfrac{21}{10}

θ = 64.53°

Now by putting the value in equation

sec^2\theta \dfrac{d\theta}{dt}=-\dfrac{21}{x^2}\dfrac{dx}{dt}

sec^264.53^{\circ} \dfrac{d\theta}{dt}=-\dfrac{21}{10^2}\times (-1)

\dfrac{d\theta}{dt}=0.038\ rad/s

Therefore rate of change in the angle is 0.038\ rad/s

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A cement block accidentally falls from rest from the ledge of a 52.9-m-high building. When the block is 14.3 m above the ground,
Anna007 [38]

Answer:

The man has at most 0.418 secs to get out of the way

Explanation:

To determine how much time at most the man has to get out of the way, we will calculate the time it will take the block to reach height 1.94m from height 14.3m.

To do this, we will first determine the time it will take the block to reach height 1.94 m from height 52.9 m and find the time it takes the block to reach height 14.3m above the ground from the same height (52.9 m), the difference is the time the man has to get out of the way.

Now, the time it will take the block to reach height 1.94 m from height 52.9 m

This means the time it will take the block to travel a height distance of 52.9m - 1.94m = 50.96m

From one of the equations of motions for free falling bodies

h = ut + 1/2(gt²)

Where h is the height

u is the initial velocity

t is the time

and g is the acceleration due to gravity (Take g = 9.8 m/s²)

From the question, the block falls from rest

∴ u = 0 m/s

h = 50.96 m

Putting these into the equation

50.96 = 0(t) + 1/2(9.8)(t²)

50.96 = 4.9t²

t² = 50.96/4.9

t² = 10.4

t = √10.4

t = 3.225 secs

This is the time it will take to reach height 1.94m (that is to reach the man)

For the time it takes the block to reach height 14.3m above the ground from height 52.9 m

That is, the time it takes the block to travel a height distance of 52.9m - 14.3m = 38.6 m

Here,

h = 38.6 m

and u = 0 m/s

Putting these into the same equation

h = ut + 1/2(gt²)

38.6 = 0(t) + 1/2(9.8)(t²)

38.6 = 4.9t²

t² = 38.6/4.9

t² = 7.878

t = √7.878

t = 2.807 secs

This is the time it takes the block to reach height 14.3 m

Now, the difference in time is 3.225secs - 2.807 secs = 0.418 secs

Hence, the man has at most 0.418 secs to get out of the way.

7 0
3 years ago
Find the kenetic energy of a car of mass 700kg racing with a velocity of 10m/s
fiasKO [112]

Answer:

35000 KJ

Explanation:

The equation for the kinetic energy is given by the formula :

E_{k} = \frac{1}{2} mv^{2}

E_{k} = \frac{1}{2} (700)(10)^{2}

E_{k} = \frac{1}{2} (700)(100)

E_{k} = (350)(100)  OR E_{k} = \frac{1}{2} (70000)

E_{k} = 35000

Units will be kilojoules since the units of mass was kilograms .

Our final answer is 35000 KJ

Hope this helped and have a good day

5 0
2 years ago
Why do the lighter isotopes disappear first from the atmosphere? Where do those isotopes go?
denpristay [2]

Lighter molecules move fast and escape from the upper atmosphere relatively quickly.

To find the answer, we have to know more about the lighter isotopes.

<h3>What are lighter isotopes?</h3>
  • Lighter molecules are mobile and soon leave the higher atmosphere.
  • A particular element's stable isotopes have slightly different atomic masses and quantum mechanical energies.
  • The lighter isotope of an element's chemical bonds are more easily broken than the heavier isotope's.
  • As a result, the light isotope typically benefits from chemical reactions.

Thus, we can conclude that, lighter molecules move fast and escape from the upper atmosphere relatively quickly.

Learn more about the isotopes here:

brainly.com/question/364529

#SPJ4

3 0
1 year ago
A 2.0 kg particle moves in a circle of radius 3.1 m. As you look down on the plane of its orbit, the particle is initially movin
Ghella [55]

Answer

given,

L(t) = 10 - 3.5 t

mass of particle = 2 Kg

radius of the circle = 3.1 m

a) torque

    τ = \dfrac{dL}{dt}

    τ = \dfrac{d}{dt}(10 - 3.5 t)

    τ = -3.5 N.m

Particle rotates clockwise as i look down the plane. Hence, its angular velocity is downward.

L decreases the angular acceleration upward. so, net torque is upward.

b) Moment of inertia of the particle

    I = m R^2

    I = 2 x 3.1²

    I = 19.22 kg.m²

    L = I ω

    ω = \dfrac{L}{I}

    ω = \dfrac{10 - 3.5 t}{19.22}

    ω = 0.520 - 0.182 t

  A = 0.52 rad/s             B = -0.182 rad/s²

5 0
3 years ago
Read 2 more answers
Which of the following is the best definition of an element?
Ostrovityanka [42]

Answer:

A. chemical substance whose atoms all have the same number of protons

Explanation:

An element is a substance which contains identical atoms that have the same number of protons in the nucleus.

Elements are arranged in the periodic table according to their atomic number (= number of protons): so atoms of different elements have a different number of protons in their nuclei.

For a neutral atom, the number of electrons around the nucleus is also equal to the number of protons.

Moreover, atoms of the same element can have a different number of neutrons, despite having the same number of protons - these atoms are called isotopes.

8 0
3 years ago
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