An object of mass 5 kg is released from rest 3000 m above the ground and allowed to fall under the influence of gravity. Assuming the force due to air resistanceis proportional to the velocity of the object with proportionality constant b = 50 N-sec/m, determine the equation of motion of the object. When will the object strikethe ground? Assume that the acceleration due to gravity is 9.81 m/secand let x(t) represent the distance the object has fallen in t seconds.dvFirst write mat = mg - bv, v(0)=v in terms of the given information.v(0) =

Given that Object mass m=5kg Released from rest 3000m above Proportionality constant b=50 N-sec/m…

Answered: An object of mass 5 kg is released from…

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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A ball is thrown upward from a height of 0.5 m at an initial speed of 32 m/sec. Acceleration resulting from gravity is -9.8m/sec². Neglecting air resistance, solve for the velocity v(t) and the height h(t) of the ball t seconds after is is thrown. Velocity v(t) Height h(t) = = meters/second meters
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A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high altitude. Assume that the air resistance is proportional to the falling velocity with the constant k = 0.6, the acceleration due to gravity g = 32ft/sec2, and that the positive direction is downward. What is the terminal velocity of the sky diver if he/she never opens the parachute?
An object at the top of a building with height 120 feet is thrown upward with an initial speed of 28 ft/s. Find its position z(t) above the ground t seconds after being thrown. (Use g = 32 ft/sec2.) z(t) = Find the time, in seconds, it takes for the object to hit the ground.
) An object is thrown upward at time t = 0. After t seconds, its height is y = −4.9t² + 2t + 4.5 meters above the ground. (a) From what height was the object thrown? (b) What is the initial velocity of the object? (c) What is the acceleration due to gravity? meters m/s m/s²
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A researcher is nuning a simulation of an upward rocket to study the upward velocity of the rocket using various fuel consumption rates. The researcher has found that the upward velocity of the rocket can be represented by the following equation, mo v = u In gt Amo-qt. where v=upward velocity of the rocket (m/s), u= the velocity at which fuel is expelled relative to the rocket (m/s), m, = the initial mass of the rocket (kg), q = the fuel consumption rate (kg/s), g = the downward accelemation of gravity (m/s), and t = time taken by the rocket for the whole motion (s). If u = 1,500 m/s, m, = 125,000 kg, q = 2,300 kg/s and g= 9.81 m/s are the values used by the researcher in one of his simulations, estimate the time, t at which v = 680 m/s using False Position method. It is known that the time, t is somewhere between 15 s and 35 s. Perform THREE (3) iterations only and calculate the approximate percent relative error, Ea| for every iteration.
a machinist is required to manufacture a square metal plate with the side length of 5cm. if the machinist is allowed an error f 0.3 cm, use differentials to estimate the error in the calculated area of the plate.

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