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
mafiozo [28]
3 years ago
13

A sky diver with a mass of 70kg jumps from an aircraft. The aerodynamic drag force acting on the sky diver is known to be Fd=kV^

2, where k=0.25N*s^2/m^2. Determine the maximum speed of free fall for the sky diver and the speed reached after 100m of fall. Plot the speed of the sky diver as a function of time and as a function of distance fallen

Physics
1 answer:
xeze [42]3 years ago
5 0

Answer:

v_{max}=52.38\frac{m}{s}

v_{100}=33.81

Explanation:

the maximum speed is reached when the drag force and the weight are at equilibrium, therefore:

\sum{F}=0=F_d-W

F_d=W

kv_{max}^2=m*g

v_{max}=\sqrt{\frac{m*g}{k}} =\sqrt{\frac{70*9.8}{0.25}}=52.38\frac{m}{s}

To calculate the velocity after 100 meters, we can no longer assume equilibrium, therefore:

\sum{F}=ma=W-F_d

ma=W-F_d

ma=mg-kv_{100}^2

a=g-\frac{kv_{100}^2}{m} (1)

consider the next equation of motion:

a = \frac{(v_{x}-v_0)^2}{2x}

If assuming initial velocity=0:

a = \frac{v_{100}^2}{2x} (2)

joining (1) and (2):

\frac{v_{100}^2}{2x}=g-\frac{kv_{100}^2}{m}

\frac{v_{100}^2}{2x}+\frac{kv_{100}^2}{m}=g

v_{100}^2(\frac{1}{2x}+\frac{k}{m})=g

v_{100}^2=\frac{g}{(\frac{1}{2x}+\frac{k}{m})}

v_{100}=\sqrt{\frac{g}{(\frac{1}{2x}+\frac{k}{m})}} (3)

v_{100}=\sqrt{\frac{9.8}{(\frac{1}{2*100}+\frac{0.25}{70})}}

v_{100}=\sqrt{\frac{9.8}{(\frac{1}{200}+\frac{1}{280})}}

v_{100}=\sqrt{\frac{9.8}{(\frac{3}{350})}}

v_{100}=\sqrt{1,143.3}

v_{100}=33.81

To plot velocity as a function of distance, just plot equation (3).

To plot velocity as a function of time, you have to consider the next equation of motion:

v = v_0 +at

as stated before, the initial velocity is 0:

v =at (4)

joining (1) and (4) and reducing you will get:

\frac{kt}{m}v^2+v-gt=0

solving for v:

v=\frac{ \sqrt{1+\frac{4gk}{m}t^2}-1}{\frac{2kt}{m} }

Plots:

You might be interested in
One has a frequency of 490 Hz and the other is 488 Hz. How many beats per second are heard?
tresset_1 [31]
When sounds at two different frequencies are combined,
two new sounds are created ... at the sum and difference
of the original frequencies.

Combining two sounds at 490 Hz and 488 Hz creates
beats at  978 Hz and 2 Hz.

The fluttering "wah wah" effect of the 2 Hz beat is much more
noticeable than the new sound at 978 Hz.
7 0
3 years ago
An airplane is initially flying horizontally (not gaining or losing altitude), and heading exactly North. Suppose that the earth
yanalaym [24]

Note: The answer choices are :

a) Increased

b) Decreased

c) stayed the same

Answer:

The correct option is Increased

The magnitude of the electric field potential difference between the wingtips increases.

Explanation:

The magnitude of the electric potential difference is the induced emf and is given by the equation:

emf = l (v \times B)

where l = length

v = velocity

B = magnetic field

As the altitude of the airplane increases, the magnetic flux becomes stronger, the speed of the airplane becomes perpendicular to the magnetic field, i.e. v \times B = vB sin90 = vB\\ ,

the induced emf = vlB, and thus increases.

The magnitude of the electric field potential difference between the wingtips increases

3 0
3 years ago
Consider a car travelling at 60 km/hr. If the radius of a tire is 25 cm, calculate the angular speed of a point on the outer edg
vlabodo [156]

To solve this problem it is necessary to apply the concepts given in the kinematic equations of movement description.

From the perspective of angular movement, we find the relationship with the tangential movement of velocity through

\omega = \frac{v}{R}

Where,

\omega =Angular velocity

v = Lineal Velocity

R = Radius

At the same time we know that the acceleration is given as the change of speed in a fraction of the time, that is

\alpha = \frac{\omega}{t}

Where

\alpha =Angular acceleration

\omega = Angular velocity

t = Time

Our values are

v = 60\frac{km}{h} (\frac{1h}{3600s})(\frac{1000m}{1km})

v = 16.67m/s

r = 0.25m

t=6s

Replacing at the previous equation we have that the angular velocity is

\omega = \frac{v}{R}

\omega = \frac{ 16.67}{0.25}

\omega = 66.67rad/s

Therefore the angular speed of a point on the outer edge of the tires is 66.67rad/s

At the same time the angular acceleration would be

\alpha = \frac{\omega}{t}

\alpha = \frac{66.67}{6}

\alpha = 11.11rad/s^2

Therefore the angular acceleration of a point on the outer edge of the tires is 11.11rad/s^2

5 0
3 years ago
???whats the answers??
OverLord2011 [107]

The answers is 30 miles per hour, the driver is speeding the car up,     section-H, 12 minutes, section-D, and 65 miles per hour.

8 0
3 years ago
How does temperature affect chemical reaction​
Elis [28]
When its temperature increases, the reactants have more kinetic energy so the frequency of effective collision increases, resulting in a faster rate of chemical reaction.
8 0
3 years ago
Other questions:
  • Scientific notation: Convert 7.1 x 10-3 to decimal notation.​
    10·1 answer
  • A skier has an acceleration of 2.5 m/s2. How long does it take her to come to a complete stop from a speed of 18 m/s? A. 3.4 s B
    12·1 answer
  • Suppose you apply a flame to heat 1 liter of water and its temperature rises by 3 C. If you apply the same flame for the same le
    8·1 answer
  • Dante is leading a parade across the main street in front of city hall. Starting at city hall, he marches the parade 4 blocks ea
    10·2 answers
  • Find the work done in pumping gasoline that weighs 6600 newtons per cubic meter. A cylindrical gasoline tank 3 meters in diamete
    11·1 answer
  • Which type of stress is a uniform stress that doesn't lead to earthquakes?
    7·2 answers
  • How would you explain digestion system using three words ??
    10·2 answers
  • A stone falls from rest from the top of a cliff,a second stone is thrown do wnward from the same height 2sec later with an initi
    15·1 answer
  • HELP!! Explain why a more streamlined car generally will have a better fuel economy than a bulkier car with the same mass.
    12·2 answers
  • Find the resultant force And angle
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!