1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
snow_tiger [21]
3 years ago
11

It is common to see birds of prey rising upward on thermals. The paths they take may be spiral-like. You can model the spiral mo

tion as uniform circular motion combined with a constant upward velocity. Assume a bird completes a circle of radius 6.00 m every 5.00 s and rises vertically at a rate of 3.00 m/s.
Physics
1 answer:
TiliK225 [7]3 years ago
6 0

Answer:

a) 8.115 m/s

b) 9.472 m/s^{2}

c) 21.7\°

Explanation:

The rest of the question is written below:

Determine (a) the bird’s speed relative to the ground; (b) the bird’s acceleration (magnitude and direction); and (c) the angle between the bird’s velocity vector and the horizontal.

<u>And we have the following data:</u>

r=6 m  is the radius of the circular path in the x-axis

T=5 s the period of the circular motion of the bird's path

V_{y}=3 m/s the vertical component of the bird's velocity, which is directed upward and is constant.

Now let's begin with the answers:

<h3>a) Bird’s speed relative to the ground</h3>

In order to find this speed, we have to calculate the magnitude of the bird's velocity vector:

V=sqrt{{V_{x}}^{2} + {V_{y}}^{2} (1)

We already know the value of V_{y}. So, we have to find V_{x}.

Since the bird is describing a circular path in the x-axis, V_{x} will be its <u>tangential velocity</u>:

V_{x}=\omega r=\frac{2 \pi}{T} r (2)

Where \omega=\frac{2 \pi}{T} is the <u>birds angular velocity</u>

V_{x}=\frac{2 \pi}{5 s} 6 m (3)

V_{x}=7.539 m/s (4)

Substituting (4) in (1):

V=sqrt{(7.539 m/s)}^{2} + (3 m/s)^{2} (5)

V=8.1147 m/s \approx 8.115 m/s (6) This is the bird's speed relative to the ground

<h3>b) Bird’s acceleration (magnitude and direction)</h3>

Since the vertical component of the bird's velocity is constant, the vertical component of its acceleration is zero:

a_{y}=0 m/s^{2}

However, the bird has radial acceleration a_{r}=a_{x} that results from its rotation on the circular path horizontally:

a_{x}=\frac{{V_{x}}^{2}}{r} (7)

a_{x}=\frac{(7.539 m/s)^{2}}{6 m} (8)

a_{x}=9.472 m/s^{2} (9) This is the magnitude of the bird's acceleration, which is directed to the center of the circular path the bird describes while it is moving upwards in the spiral.

<h3>c) Angle between the bird’s velocity vector and the horizontal</h3>

In order to find the direction of the bird's velocity vector with the horizontal, we have to find the angle between the horizontal and the vertical component of this velocity:

\theta=tan^{-1}(\frac{V_{y}}{V_{x}}) (10)

\theta=tan^{-1}(\frac{3 m/s}{7.539 m/s}) (11)

Finally:

\theta=21.69\° \approx 21.7 \° (12)

You might be interested in
Consider a compact car that is being driven
tigry1 [53]
The answer is 2847.830m
6 0
2 years ago
Precision measurements of the acceleration due to gravity show that the acceleration is slightly different in different location
DochEvi [55]
Gravity largely depends on the comparison of two objects; it's why you have the equation F= (GMm)/r^2. On Earth, you have different altitudes that, with the formula, will give different results for gravity because the radius is different everywhere. This difference on calculations, however, are seen to be miniscule. We know gravity as 9.81 m/s^2 but it might be different by thousandths or hundreds of thousandths of a decimal.
6 0
3 years ago
Read 2 more answers
Why is Earth’s North Pole a geographic north pole but a south seeking pole magnetically?
natima [27]

Answer:It is actually the South Magnetic pole

Explanation:The magnetic pole near earth's geographic north pole is actually the south magnetic pole. When it comes to magnets, opposites attract. This fact means that the north end of a magnet in a compass is attracted to the south magnetic pole, which lies close to the geographic north pole.

3 0
3 years ago
What do fuel cells, batteries and, solar cells have in common A.the all produce static electricity B. they are all sources of di
Vaselesa [24]
The correct answer is B :)
3 0
3 years ago
Read 2 more answers
2
taurus [48]
A the endocrine system does not fulfill its function
5 0
2 years ago
Other questions:
  • The force needed to accelerate a stationary 2000 racing car to a speed of 144 km/h in a distance of 80 meters
    14·1 answer
  • At which boundary does subduction stop occurring, resulting in a mountain range?
    6·2 answers
  • Why must you balance an equation to describe correctly what happens in a chemical reaction
    7·1 answer
  • How many protons does this atom have?
    15·2 answers
  • Which statements describe the sun? Check all that apply
    8·2 answers
  • Height of a artificial satelite​
    12·1 answer
  • When two stars are bound together gravitationally and orbit a common mass, they're known as
    12·1 answer
  • 2. A block of mass 1.2 kg lies on a frictionless surface. A man slides the block
    14·1 answer
  • The gravitational force between two volleyball players is 3.3x10^-7.
    9·1 answer
  • At what height from the surface of earth will the value of 'g' reduced to 64% from the value at the surface? Radius of earth = 6
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!