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svet-max [94.6K]
3 years ago
15

A sky diver of mass 53 kg can slow herself to a constant speed of 95 km/h by orienting her body horizontally, looking straight d

own with arms and legs extended. In this position, she presents the maximum cross-sectional area and thus maximizes the air-drag force on her.
(a) What is the magnitude of the drag force on the sky diver?
N
(b) If the drag force is equal to bv2, what is the value of b?
kg/m
(c) At some instant she quickly flips into a "knife" position, orienting her body vertically with her arms straight down. Suppose this reduces the value of b to 55 percent of the value in Parts (a) and (b). What is her acceleration at the instant she achieves the "knife" position?
m/s2
Physics
1 answer:
Nady [450]3 years ago
7 0

Answer:

force = 520 N

b = 0.747 kg/m

acceleration = 4.41 m/s²    

Explanation:

given data

mass = 53 kg

speed = 95 km/h

solution

as here driver is at constant speed so here drag force is

drag force = mg

force = 53 × 9.81

force = 520 N

and when drag force is equal to bv²

b = \frac{mg}{v^2}  

b = \frac{520}{26.38}  

b = 0.747 kg/m

and

here x = 520 × 0.55  = 286 N

so here

F net = 520 - 286

F net = 234 N

so here

acceleration = \frac{F \ net}{m}  

acceleration = \frac{234}{53}  

acceleration = 4.41 m/s²    

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The first part of the question is not complete and it is;

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B) A1 = 50 and A2 = 1,800,000

C) Capacitor Current is given by the expression;

I = e^(-4000t)[0.95 - 1800t]

Explanation:

A) In capacitors, Energy stored is given as;

U = (1/2)Cv²

Where C is capacitance and v is voltage.

So initial kinetic energy;

U(0) = (1/2)C(vo)²

From the question, C = 250 nF and v = 50V

So, U(0) = (1/2)(250 x 10^(-9))(50²) = 0.3125 x 10^(-3)J = 0.3125 mJ

B) from the question, we know that;

A1e^(-4000t) + (A2)te^(-4000t)

So, v(0) = A1e^(0) + A2(0)e^(0)

v(0) = 50

Thus;

50 = A1

Now for A2; let's differentiate the equation A1e^(-4000t) + (A2)te^(-4000t) ;

And so;

dv/dt = -4000A1e^(-4000t) + A2[e^(-4000t) - 4000e^(-4000t)

Simplifying this, we obtain;

dv/dt = e^(-4000t)[-4000A1 + A2 - 4000A2]

Current (I) = C(dv/dt)

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