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MakcuM [25]
3 years ago
14

The terminal velocity of a person falling in air depends upon the weight and the area of the person facing the fluid. Find the t

erminal velocity (in meters per second and kilometers per hour) of an 80.0-kg skydiver falling in a pike (headfirst) position with a surface area of 0.140 m2
Physics
1 answer:
Serga [27]3 years ago
4 0

Answer:

115 m/s, 414 km/hr

Explanation:

There are two forces acting on a skydiver: gravity and air resistance (drag).  At terminal velocity, the two forces are equal and opposite.

∑F = ma

D − mg = 0

D = mg

Drag force is defined as:

D = ½ ρ v² C A

where ρ is the fluid density,

v is the velocity,

C is the drag coefficient,

and A is the cross sectional surface area.

Substituting and solving for v:

½ ρ v² C A = mg

v² = 2mg / (ρCA)

v = √(2mg / (ρCA))

We're given values for m and A, and we know the value of g.  We need to look up ρ and C.

Density of air depends on pressure and temperature (which vary with elevation), but we can estimate ρ ≈ 1.21 kg/m³.

For a skydiver falling headfirst, C ≈ 0.7.

Substituting all values:

v = √(2 × 80.0 kg × 9.8 m/s² / (1.21 kg/m³ × 0.7 × 0.140 m²))

v = 115 m/s

v = 115 m/s × (1 km / 1000 m) × (3600 s / hr)

v = 414 km/hr

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NikAS [45]

Answer:

a) velocity v = 322.5m/s

b) time t = 19.27s

Explanation:

Note that;

ads = vdv

where

a is acceleration

s is distance

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Given;

a = 6 + 0.02s

so,

\int\limits^s_0 {a} \, ds  = \int\limits^v_0 {v} \, dv\\ \int\limits^s_0 {6+0.02s} \, ds  = \int\limits^v_0 {v} \, dv\\ 6s + \frac{0.02s^{2} }{2} = \frac{1}{2} v^{2} \\v = \sqrt{12s + 0.02s^{2} } .....................1 \\\\\\

Remember that

v = \frac{ds}{dt} \\\frac{ds}{v} = dt\\\int\limits^s_0 {\frac{ds}{\sqrt{12s+0.02s^{2} } } } \, ds = \int\limits^t_0 {} \, dt \\t=  (5\sqrt{2} ) ln  \frac{| [s + 300 + \sqrt{(s^{2}  + 600s)} ] |}{300} .......2

substituting s = 2km =2000m, into equation 1

v = 322.5m/s

substituting s = 2000m into equation 2

t = 19.27s

8 0
3 years ago
A ball is fired at an angle of 45 degrees, the angle that yields the maximum range in the absence of air resistance. What is the
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3 years ago
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A block is pulled across a flat surface at a constant speed using a force of 50 newtons at an angle of 60 degrees above the hori
vladimir2022 [97]

The magnitude of the friction force is 25 N

Explanation:

To solve this problem, we just have to analyze the forces acting on the block along the horizontal direction. We have:

  • The horizontal component of the pulling force, F cos \theta, where F = 50 N is the magnitude and \theta=60^{\circ} is the angle between the direction of the force and the horizontal; this force acts in the  forward direction
  • The force of friction, F_f, acting in the backward direction

According to Newton's second law, the net force acting on the block in the horizontal direction must be equal to the product between the mass of the block and its acceleration:

\sum F_x = ma_x

where

m is the mass of the block

a_x is the horizontal acceleration

However, the block is moving at constant speed, so the acceleration is zero:

a_x = 0

So the equation becomes

\sum F_x = 0 (1)

The net force here is given by

\sum F_x = F cos \theta - F_f (2)

And so, by combining (1) and (2), we find the magnitude of the friction force:

F cos \theta - F_f = 0\\F_f = F cos \theta = (50)(cos 60^{\circ})=25 N

Learn more about  force of friction:

brainly.com/question/6217246

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brainly.com/question/3017271

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4 0
3 years ago
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saw5 [17]
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•Sustainable Seed and Plant Varieties
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A "biconvex" lens is one in which both surfaces of the lens bulge outwards. Suppose you had a biconvex lens with radii of curvat
Stolb23 [73]

Answer: f=150cm in water and f=60cm in air.

Explanation: Focal length is a measurement of how strong light is converged or diverged by a system. To find the variable, it can be used the formula:

\frac{1}{f} = (nglass - ni)(\frac{1}{R1} - \frac{1}{R2}).

nglass is the index of refraction of the glass;

ni is the index of refraction of the medium you want, water in this case;

R1 is the curvature through which light enters the lens;

R2 is the curvature of the surface which it exits the lens;

Substituting and calculating for water (nwater = 1.3):

\frac{1}{f} = (1.5 - 1.3)(\frac{1}{10} - \frac{1}{15})

\frac{1}{f} = 0.2(\frac{1}{30})

f = \frac{30}{0.2} = 150

For air (nair = 1):

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f = \frac{30}{0.5} = 60

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In air, f = 60cm.

5 0
3 years ago
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