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raketka [301]
3 years ago
12

A car comes to a bridge during a storm and finds the bridge washed out. The driver must get to the other side, so he decides to

try leaping it with his car. The side the car is on is 20.5 m above the river, whereas the opposite side is a mere 2.4 m above the river. The river itself is a raging torrent 57.0 m wide.
A) How fast should the car be traveling just as it leaves the cliff in order just to clear the river and land safely on the opposite side?
B) What is the speed of the car just before it lands safely on the other side?
Physics
1 answer:
dybincka [34]3 years ago
7 0

Answer:

(A) Velocity of car in order just to clear the river and land safely on the opposite side is 29.68 \frac{m}{s}

(B) The speed of the car is 35.14 \frac{m}{s}

Explanation:

Given:

Car distance from river y = 20.5 m

Mere distance from river y_{o} = 2.4 m

River length x= 57 m

(A)

For finding the velocity of car,

Using kinematics equation we find velocity of car

  y - y_{o} = v_{o}t + \frac{1}{2} gt^{2}

Where v_{o} = 0, g = 9.8 \frac{m}{s^{2} }                                     ( given in question )

20.5 - 2.4 = \frac{1}{2} \times 9.8  \times t^{2}

   t= 1.92 sec

The speed of the car before it lands safely on the opposite side of the river is given by,

   v_{x}  = \frac{x-x_{o} }{t}

   v_{x}  = \frac{57-0}{1.92}                        ( x_{o} = 0 )

   v_{x} = 29.68 \frac{m}{s}

(B)

For finding the speed,

The horizontal distance travel by car,

  v_{y} = v_{o} + at

Where a = 9.8 \frac{m}{s^{2} }

  v_{y} = 9.8 \times 1.92

  v_{y} = 18.81 \frac{m}{s}

For finding the speed,

  v = \sqrt{v_{x}^{2} + v_{y} ^{2}    }

  v = \sqrt{(29.68)^{2}+ (18.81)^{2}  }

  v = 35.14 \frac{m}{s}

Therefore, the speed of the car is 35.14 \frac{m}{s}

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g The electric power needs of a community are to be met by windmills with 40-m-diameter rotors. The windmills are to be located
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Answer:

Explanation:

Given Data

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Required power output is:  P ₀ = 2100 k W

Expression to calculate the exergy of the air is

E = V ² / 2

Substitute the value in above expression

E = ( 6 m / s ) ² / 2

E = 18 m ² / s ² x (1kJ/kg / 1000m²/s²)

E = 0.018 k J / k g

Expression to calculate the density of the air is

P v =m R T

m /v = P  /RT ⋯ ⋯( I )

Here  

m  is the mass of the air,  

v  is the volume of the air,  

P  is the atmospheric pressure,  

T  is the standard temperature at the atmospheric pressure and  

R  is the gas constant

As the density is

ρ = m /V

Substitute the value in expression (I)

ρ = 101  kP a /( 0.287 k J / k g ⋅ K ) ( 298 K )

ρ = 1.180 k g / m ²

Expression to calculate the mass flow rate is

m = ρ A V ⋯ ⋯ ( I I )

Here  A  is the area of the windmill

Expression to calculate the  A  is

A = π /4  d ²

Substitute the value in above expression

A = π /4 ( 40 m ²)

A = 1256.63 m ²

Substitute the value in expression (II)

m = ( 1.180 k g / m ³) ( 1256.63 m ²) ( 6 m / s )

m = 8896.94  k g / s

Expression to calculate the maximum power available to the windmill is

P w = m ( V ² /2 )

Substitute the value in above expression

P w = 8896.94  k g / s ( (6m/s)²/2 )

P w = 160144.92 W  × ( 1 W /1000 k W )

P w = 160.144 k W

Expression to calculate the number of windmills required is

n = P o /P w

Substitute the value in above expression

n=2100kw/160.144kw

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A sample of helium has a volume of 12.7 m3. The temperature is raised to 323 K at which time the gas occupies 32.5 m3? Assume pr
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Answer: The original temperature was

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Explanation:

Let's put the information in mathematical form:

V_{1}=12.7m^{3}

T_{1}=?

V_{2}=32.5m^{3}

T_{2}=323K

P_{1}=P_{2}=3atm

If we consider the helium as an ideal gas, we can use the Ideal Gas Law:

PV=nRT

were <em>R</em> is the gas constant. And <em>n</em> is the number of moles (which we don't know yet)

From this, taking R=0.08205746\frac{atm.l}{mol.K},  we have:

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Now:

T_{1}=\frac{P_{1}V_{1}}{nR}

⇒T_{1}=126.51K

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