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
Decribir los tejidos que forman en triceps, gluteo, deltroides. ​
Genrish500 [490]

Answer:The deltoid is a muscle in the shoulder It has the shape of a hollow semi-cone

Explanation:

7 0
2 years ago
What is the minimal mass of helium (density 0.18 kg/m3) needed to lift a balloon carrying two people in a basket, if the total m
Sergio039 [100]

Answer:   
 M[min] = M[basket+people+ balloon, not gas] * ΔR/R[b] 
 Î”R is the difference in density between the gas inside and surrounding the balloon. 
 R[b] is the density of gas inside the baloon.   
 ==================================== 
 Let V be the volume of helium required. 
 Upthrust on helium = Weight of the volume of air displaced = Density of air * g * Volume of helium = 1.225 * g * V   
 U = 1.225gV newtons 
 ---- 
 Weight of Helium = Volume of Helium * Density of Helium * g 
 W[h] = 0.18gV N   
 Net Upward force produced by helium, F = Upthrust - Weight = (1.225-0.18) gV = 1.045gV N  -----

 
 Weight of 260kg = 2549.7 N 
 Then to lift the whole thing, F > 2549.7 
 So minimal F would be 2549.7 
 ---- 
 1.045gV = 2549.7 
 V = 248.8 m^3   
 Mass of helium required = V * Density of Helium = 248.8 * 0.18 = 44.8kg (3sf)   
 =====   
 Let the density of the surroundings be R 
 Then U-W = (1-0.9)RgV = 0.1RgV   
 So 0.1RgV = 2549.7 N 
 V = 2549.7 / 0.1Rg   
 Assuming that R is again 1.255, V = 2071.7 m^3 
 Then mass of hot air required = 230.2 * 0.9R = 2340 kg   
 Notice from this that M = 2549.7/0.9Rg * 0.1R so   
 M[min] = Weight of basket * (difference in density between balloon's gas and surroundings / density of gas in balloon)   
 M[min] = M[basket] * ΔR/R[b]
3 0
3 years ago
On a planet where g = 10.0 m/s2 and air resistance is negligible, a sled is at rest on a rough inclined hill rising at 30°. The
Cloud [144]

Answer:

Explanation:

a is the acceleration

μ is the coefficient of friction

Acceleration of the object is given by

a = g (\sin  \theta -\mu \cos \theta)\\\\=10( \sin 30 - 0.4 \cos 30)\\\\=10(0.5-0.3464)\\\\=1.54m/s^2

Velocity at the bottom

v^2=u^2+2as\\\\u=0\\\\v^2=2as\\\\=2*1.54*8\\\\=24.576\\\\v=4.96m/s

after travelling 4m , its velocity becomes 0

a=\frac{v^2-u^2}{2s}

a=\frac{0-u^2}{2s}

a=\frac{-(-4.96)^2}{2*4} \\\\=-3.075m/s^2

Coefficient of kinetic friction

μ = F/N

=\frac{ma}{mg} \\\\=\frac{3.075}{10} \\\\=0.31

Therefore, the Coefficient of kinetic friction is 0.31

8 0
2 years ago
Read 2 more answers
A steam engine absorbs 4 x 105 J and expels 3.5 x 105 J in each cycle. What is its efficiency?
Wewaii [24]
Input heat, Qin = 4 x 10⁵ J
Output heat, Qout = 3.5 x 10⁵ J

From the first Law of thermodynamics, obtain useful work performed as
W = Qin  -  Qout
     = 0.5 x 10⁵ J

By definition, the efficiency is
η = W/Qin
   = 100*(0.5 x 10⁵/4 x 10⁵)
   = 12.5%

Answer: The efficiency is 12.5%
3 0
3 years ago
A particle is moving along the x-axis so that its position at any time t is greater than and equal to 0 is given by x(t)=2te^-t?
erastovalidia [21]
For speed you can differentiate the equation, for acceleration you can again differentiate the equation .
at t=0 the particle is slowing down , when you get equation for velocity put t=0 then only -1 is left
6 0
3 years ago
Other questions:
  • Explain why ice cubes formed from water of a glacier freeze at a higher temperature than ice cubes
    12·1 answer
  • Planet geos in orbit a distance of 1
    7·2 answers
  • Calculate the speed of an object that tavels 62.43m in 38.4s
    8·1 answer
  • ASAP answer all pls will mark brainiest
    10·2 answers
  • A block of mass 2 kg is placed on the floor. The coefficient of static friction is 0.4. A horizontal force of 2.5 N is applied o
    11·1 answer
  • A car covers 72 kilometers in the first hour of its journey. In the next hour, it covers 90 kilometers. What is the amount of wo
    14·1 answer
  • What is the philosopher’s stone
    15·1 answer
  • A 50 kg boy runs and jumps with a forward velocity of 1.5 m/s into a 125 kg stationary boat.
    12·2 answers
  • The splitting of an atom to produce energy is called a ________ reaction.
    5·2 answers
  • What happend to the egg in the fresh water glass?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!