Interested to Buy Any Domain ? << Click Here >> for more details...
DIFFERENTIAL EQUATIONS - EXAMPLE 20.2 : During the landing process of an airplane, the velocity is constant at v. (a) If the displacement of the plane is x at time t, find the differential equation that relates t, x and v. (b) The plane has 2 parts of wheels - the front and the back, separated by a distance L. The front part of the wheel touches the land first, that allows the straight body of the plane to form an angle T with the horizontal land. If the vertical distance between the back part of the wheel and the horizontal land is y, find the equation of y as a function of L and T. (c) Find the differential equation that relates dy as a function of dt, v and sin T. (d) Find the differential equation that consist of dy as a function of y, L, v and dt. (e) Find the equation of y as a function of v, L, t and C where C is a constant. (f) When t = 0, prove that y = exp C as the initial value of y.
- 1 Answers
- 2667 Views
- I also Faced
- E-Mail Answers
Answer Posted / kangchuentat
DIFFERENTIAL EQUATIONS - ANSWER 20.2 : (a) The kinematic relationship is dx = v dt. (b) The trigonometric relationship is sin T = y / L. (c) y = -vt sin T, then dy = -v dt sin T since y / x = sin T and x = -vt for y is decreased with an increasing x. (d) dy = -v dt sin T = -v dt (y / L) = -y (v / L) dt. (e) dy / y = (-v / L) dt. Integrate both sides of equation will produce ln y = -vt / L + C, then y = exp (-vt / L + C) = (exp C) exp (-vt / L). (f) When t = 0, y = (exp C) exp (-vt / L) = (exp C) exp (0) = exp C. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
| Is This Answer Correct ? | 0 Yes | 0 No |
Post New Answer View All Answers
Explain how can you determine the largest impeller that a pump can handle?
what is mean by chemical engineering and its scope in industry
Is it advisable to cool a fin fan by spraying demineralized water on it?
Explain the different types of equipments for the conveyance of solids?
When should one be concerned with the tube wall temperature on the cooling waterside of a shell and tube exchanger?
What is load?
How fouling effected the heat transfer rate?
What are the merits of using a falling film evaporator?
What is pneumatic conveying?
What are the Major Utility Systems in a Pharma Plant? How are they interrelated?
What are the advantages of using gear pumps?
Explain what are some good uses of low-grade steam at 12 atm and 1920c?
What is the best way to configure a bypass line in slurry services?
Explain the advantages of using a ball mill over other conventional methods of crushing?
Explain what information is needed to specify a mixer?
