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Alborosie
3 years ago
13

A Boeing 787 is initially moving down the runway at 6.0 m/s preparing for takeoff. The pilot pulls on the throttle so that the e

ngines give the plane a constant acceleration of 1.9 m/s2. The plane then travels a distance of 1700 m down the runway before lifting off. How long does it take from the application of the acceleration until the plane lifts off, becoming airborne
Physics
1 answer:
andrey2020 [161]3 years ago
3 0

Answer:

39.26 s

Explanation:

From the question given above, the following data were obtainedb

Initial velocity (u) = 6 m/s

Acceleration (a) = 1.9 m/s²

Distance travelled (s) = 1700 m

Time (t) =?

Next, we shall determine the final velocity of the plane. This can be obtained as follow:

Initial velocity (u) = 6 m/s

Acceleration (a) = 1.9 m/s²

Distance travelled (s) = 1700 m

Final velocity (v) =?

v² = u² + 2as

v² = 6² + (2 × 1.9 × 1700)

v² = 36 + 6460

v² = 6496

Take the square root of both side

v = √6496

v = 80.6 m/s

Finally, we shall determine the time taken before the plane lifts off. This can be obtained as follow:

Initial velocity (u) = 6 m/s

Acceleration (a) = 1.9 m/s²

Final velocity (v) = 80.6 m/s

Time (t) =?

v = u + at

80.6 = 6 + 1.9t

Collect like terms

80.6 – 6 = 1.9t

74.6 = 1.9t

Divide both side by 1.9

t = 74.6 / 1.9

t = 39.26 s

This, it will take 39.26 s before the plane lifts off.

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

The voltage across the terminals of a 250 nF capacitor is 50 V, A1e^(-4000t) + (A2)te^(-4000t) V, t0, What is the initial energy stored in the capacitor? Express your answer to three significant figures and include the appropriate units. t

Answer:

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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)

I = (250 x 10^(-9))e^(-4000t)[-4000A1 + A2 - 4000tA2]

Thus, Initial current (Io) is;

Io = (250 x 10^(-9))[e^(0)[-4000A1 + A2]]

We know that Io = 400mA from the question or 0.4 A

Thus;

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0.4 = 0.001A1 - (250 x 10^(-9)A2)

Substituting the value of A1 = 50V;

0.4 = 0.001(50) - (250 x 10^(-9)A2)

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