6. An object is dropped from the top of a building 200 m high. The object encountersair resistance which is proportional to its velocity v(t) with constant of proportionality9.8 kg/sec and acceleration due to gravity g = 9.8 m/sec².(a) Set up and solve the initial value problem for the velocity of the object v(t) at timet.(b) If y(t) is the distance traveled by the object in t seconds, set up and solve theinitial value problem for y(t).

Answered: 6. An object is dropped from the top of…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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العنوان оне hot small copper ball [c in kJ/kg.°C, k in W/m.°C] is suddenly placed in water maintained at 100 °C. The convection heat transfer coefficient is h in W/m². ºC. Derive equation to calculate the time required to reduce ball to temperature T.
C (a) Write down the equation of motion for the point particle of mass m moving in the Kepler potential U(x) = -A/x+B/x² where x is the particle displacement in m. (b) Introduce a dissipative term in the equation of motion assuming that the dissipative force acting on a particle is proportional to the partical velocity with the coefficient of proportionality v. Write down the modified equation of motion. From the dimensionless equation of motion modified by dissipation Compare to question (2 b) derive a linearised equation of motion around a stable equilibrium state. Solve it and determine what is the range of values of the free parameter B for which the particle motion is oscillatory or non-oscillatory? What is the critical value of that determines a transition from the subcritical case with the oscillatory motion to the super-critical case with the non-oscillatory motion?
A body moving along the x axis starts at position x = 0 at t = 0, and moves with velocity v(t) = at³ + bt + c. Find: (1) its acceleration as a function of time, and (2) its position as a function of time. Acceleration: a(t) = Position: r(t)
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A particle moving along a straight line has acceleration a(t) = 12t + 10 (measured in m/s2) and initial velocity v(0) = -4 m/s. (a) , Find the velocity at time t. Show your work. (b) Find the distance traveled during the time interval [1,3] . Show your work. (c) Find the average velocity during the time interval [1,3] . Show your work. (d) .. Sketch a possible graph of the position function. Annotate your plot.
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A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the mass is released from rest from a point 4 inches below the equilibrium position Give the initial conditions. (Use g = 32 ft/s² for the acceleration due to gravity.) x(0) = x'(0) = xx(t) = ft Find the equation of motion. ft ft/s
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