Question

Suppose an object falling in the atmosphere has mass m=10kg and the drag coefficient is γ=2kg/s. Recall that the differential equation governing the motion of the particle is given by mv′=mg−γv(∗). If the velocity of the object at time t=0s is v(0)=9.25m/s, find the solution of the differential equation given in (∗) corresponding to this initial value (use g=9.8 and do not worry about units), Answer: v(t)= find the velocity of the object at time t=0.5s (be sure to enter units). Answer: $

Answer 1

Answer:

The required equation is

V = 49 - e ^((t + 18.4)/5)

At t = 0.5, V = 5.18m/s.

The solution to the ODE required rearrangement of the given equation with the like terms on the same side and then integrating using the initial value for v to find the value of the constant term.

Explanation:

The detailed solution can be found below.