Answer:
A. Velocity = 28.61m/s
B. Maximum velocity = 100m/s
Explanation:
Remember that acceleration due to gravity, a is the change in velocity divided by the change in time
a(t) = dv/dt
This equation can be written as
dt = (1/a(t))dv
Integrating both sides
Integral(dt) = integral((1/a(t))dv)
Inputting a = 9.81[1 - v^2(10^4)]
Integral(dt) = integral((1/9.81[1 - v^2(10^-4)]dv)
t = 50/9.81 * Ln[(1 + 0.01v)/(1 - 0.01v)]
Making v the subject of formula,
v = (100 * [(exp(0.1962*t) - 1)/(exp(0.1962*t) + 1)])
A. t = 3s
v = (100 * [(exp(0.5886) - 1)/(exp(0.5886) + 1])
= 28.61 m/s
B. At t = infinity
Vmax = 100m/s
Attached the steps in the integration for better understanding.