2. Skydiving If a body of mass m falling from rest under the action of gravityencounters an air resistance proportional to the square of velocity, then the body'svelocity t seconds into the fall satisfies the equationdvdtm= mg - kv2, k>0where k is a constant that depends on the body's aerodynamic properties and thedensity of the air. (We assume that the fall is too short to be affected by changes inthe air's density.)a) 10 sb) 100 sc) 1000 sFind the velocity of an object with a mass of 10 kg and a value of k = 0.05 N.s/mafter:

Given that a body of mass m falling from rest under the action of gravity.The differential equation…

Answered: Skydiving If a body of mass m falling…

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 800-lb object is released from rest 600 ft above the ground and allowed to fall under the influence of gravity. Assuming that the force in pounds due to air resistance is - 20v, where v is the velocity of the object in ft/sec, determine the equation of motion of the object. When will the object hit the ground? Assume that the acceleration due to gravity is 32 ft / sec and let x(t) represent the distance the object has fallen in t seconds. Determine the equation of motion of the object. x(t) = O
t If the velocity of a moving object is y(t) = -- X 2 2 in meters per second, then what is its displacement, in meters, from t=2 to 5 seconds? 1²
A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x from x = -1 to x = 1. The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is 9.8 and the density of water is 1000 kg m³ m s²
A model for the position x(t) of an Olympic jump skier says that the acceleration a(t) = x" is proportional to the square of the velocity v(t) = x'(t). Note this model comes from taking into account the friction of air against the skier, and we are greatly simplifying the problem by not taking into account gravity. In this problem, units of distance are in meters and units of 1. time are in seconds. (a) Give an ODE in terms of v(t) only (meaning: no x or a) that corresponds to this model, and find its general solution v. (b) Recalling that our model comes from taking friction into account, which will slow down the skier, say whether you expect your proportionality constant from la to be positive or negative. (c) Use your solution v(t) from la to find x(t). (d) Use the initial conditions' x(0) = 0 and v(0) = 100 to find the unique solution for x(t), the position of the skier. (e) Assume for simplicity the following information: the skiers take 8 seconds before reaching the ground after…
Analytical Solution to the Falling Parachutist Problem Problem Statement. A parachutist of mass 68.1 kg jumps out of a stationary hot air bal- loon. Use Eq. (1.10) to compute velocity prior to opening the chute. The drag coefficient is equal to 12.5 kg/s.
At 7 pm on a Wednesday evening. Mr Huxley's water tank was full. The capacity of the tank was 3 000 litres. Unfortunately, the tap on the tank was leaking in such a way that the change in volume at any time (r) hours was proportional to the volume (V) of the tank. This means that AP =-kV . dt Show that V= Ve is a solution of this equation. Given that the volume of the tank after 3 hours is 1900 litres, show that k = 0.1523 correct to 4 decimal places. (iii) By the time Mr Huxley discovered that the tank was leaking, there were only 250 litres of water remaining. At what time and on which day did Mr Huxley discover the leak (Answer correct to the nearest minute)?
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