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denis-greek [22]
3 years ago
12

On a journey of 600 km, a train was delayed 1 hour and 30 min after having covered 1 4 of the way. To arrive on time at the dest

ination, the engine driver had to increase the speed by 15 km/hour. How long did the train travel for
Physics
1 answer:
mars1129 [50]3 years ago
5 0

Answer:

The train travelled 10hours.

Explanation:

Using speed= distance/time ...eq1

Let the time taken by train to cover the journey be t.

Let the speed of train be s

Time= distance/speed ...eq2

Time t =600/s ...eq3

The train is delayed for 1 1/2 hours=3/2 hours

Train increased by 15km/hr.

Train travelled 1/4 of 600k.= 150km.

Speed increased by s + 15 to cover the remaining 450km

t = 150/s + 400/(s + 15) + 3/2 ..eq4

Equating eq3 and 4

600/s= 150/s + 460/(s + 15) + 3/2

450/s = 3/2 + 450/(s + 15)

3s^2 + 45s -13500=0

Solving the quadratic equation

S= -45 +-sqrt(45^2-4(3×13500)/2×3

S= 60 , -75

Hence speed of train is 60km/hr

Using eq 2 distance/speed=time

600/60=10

t= 10hours

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Answer:

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The aqueduct passes under Johnson Road in Lancaster through a siphon. The maximum capacity of the aqueduct is 350 m3/s. The heig
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Answer:

D ≈ 8.45 m

L ≈ 100.02 m

Explanation:

Given

Q = 350 m³/s (volumetric water flow rate passing through the stretch of channel, maximum capacity of the aqueduct)

y₁ - y₂ = h = 2.00 m (the height difference from the upper to the lower channels)

x = 100.00 m (distance between the upper and the lower channels)

We assume that:

  • the upper and the lower channels are at the same pressure (the atmospheric pressure).
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  • y₁ = 2.00 m  (height of the upper channel)
  • y₂ = 0.00 m  (height of the lower channel)
  • g = 9.81 m/s²
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We apply Bernoulli's equation as follows between the point 1 (the upper channel) and the point 2 (the lower channel):

P₁ + (ρ*v₁²/2) + ρ*g*y₁ = P₂ + (ρ*v₂²/2) + ρ*g*y₂

Plugging the known values into the equation and simplifying we get

Patm + (1000 Kg/m³*(0 m/s)²/2) + (1000 Kg/m³)*(9.81 m/s²)*(2 m) = Patm + (1000 Kg/m³*v₂²/2) + (1000 Kg/m³)*(9.81 m/s²)*(0 m)

⇒ v₂ = 6.264 m/s

then we apply the formula

Q = v*A  ⇒   A = Q/v ⇒   A = Q/v₂

⇒   A = (350 m³/s)/(6.264 m/s)

⇒   A = 55.873 m²

then, we get the diameter of the pipe as follows

A = π*D²/4   ⇒   D = 2*√(A/π)

⇒   D = 2*√(55.873 m²/π)

⇒   D = 8.434 m ≈ 8.45 m

Now, the length of the pipe can be obtained as follows

L² = x² + h²

⇒ L² = (100.00 m)² + (2.00 m)²

⇒ L ≈ 100.02 m

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