An object of mass 2020 kg is released from rest 30003000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistance is proportional to the velocity of the object with proportionality constant bequals=5050 N-sec/m, determine the equation of motion of the object. When will the object strike the ground? Assume that the acceleration due to gravity is 9.81 m divided by sec squared9.81 m/sec2 and let x(t) represent the distance the object has fallen in t seconds

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

F(t) = 50x'(t)  (1)

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

F(t) = mx''(t) = 50x''(t)

As the mass was released from rest, the acceleration is the gravity, and

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

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

Replacing in (1) we get

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

and

x'(t) = -9.81 m/sec

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

x(t) = -9.81*t  + C  

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

C = 3000

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

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

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

1 3 5

step-by-step explanation:

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