Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.An object of mass 5 kg is given an initial downward velocity of 50 m/sec and then allowed to fall under the influence of gravity. Assume that the force in newtons due to air resistance is -10v, where y is the velocity of the object in m/sec. Determine the equation of motion of the object. If the object is initially 500 m above the ground, determine when the object will strike the ground.
Solution:Step 1:The objective of this question is to determine when the object will strike on the floor.Step 2:Given that:Mass =m =5kgInitial velocity = V0 =50b = 10 N-sec/mg= 9.81 m/sec2.v0 = 500mStep 3:Applying the first order Newton differential equationa). mTo illuminate this condition, we misuse a procedure called partition of factors, regarding dv and dt as differentials, so we can revise the equations(a) Hence, the nomenclature the separation of equation:b). Now, integrated the separated equation=c). The derivative of given equation isBecauseOr Here the new steady A has extent e-bc and a similar sign() as(mg-bv). Unraveling for v, we acquired). v= This condition is called as general answer for the differential condition: In particular case, we would be given the estimations of m, g and b. To decide the consistent A when all is said in done arrangement, we can utilize the underlying speed of the protest v0. That is, we tackle the underlying quality issue.mSubstituting v=v0 and t=0 into the general answer for the differential condition, we can settle for A. with this incentive for A, the answer for the underlying worth issue is: