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Svetradugi [14.3K]
3 years ago
9

What is the answer to #3?

Mathematics
1 answer:
omeli [17]3 years ago
3 0
Letter D is probably the right answer
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Step-by-step explanation:

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An object of mass 2020 kg is released from rest 30003000 m above the ground and allowed to fall under the influence of gravity.
Liono4ka [1.6K]

Answer:

Equation of motion

x(t) = -9.81*t  + 3000

The object will strike the​ ground in 305.81 sec

Step-by-step explanation:

a) Determine the equation of motion of the object

If x(t) repsent the distance the object has fallen in t seconds, then we have x'(t) and x''(t) represent the speed and acceleration respectively.

Since the force due to air resistance is proportional to the velocity of the object with proportionality constant b = 50 N-sec/m, we have

<em>F(t) = 50x'(t)  </em>(1)

Due to Newton's 2nd law of motion (assuming the mass remains constant )

<em>F(t) = mx''(t) = 50x''(t) </em>

As the mass was released from rest, <em>the acceleration is the gravity</em>, and

<em>F(t) = 50*(-9.81) = -490.5 N/m </em>

The negative sign is due to the fact that the mass is falling downwards.

Replacing in (1) we get

<em>-490.5 = 50x'(t) ===> x'(t) = -9.81 m/sec </em>

and

<em>x'(t) = -9.81 m/sec </em>

This is a simple differential equation which can be solved directly by integration

<em>x(t) = -9.81*t  + C  </em>

where C is a constant, but we know that x(0) = 3000 m, so

<em>C = 3000 </em>

We then have our final equation of motion which is

x(t) = -9.81*t  + 3000

b) When will the object strike the​ ground?

The object will strike the ground for the instant t for which x(t) = 0

<em>x(t) = 0 ===> 9.81*t = 3000 ===> t = 3000/9.81 ===> </em><em>t = 305.81 sec </em>

3 0
3 years ago
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