Hi, I have a past exam questions that I need help with solving. I am having some difficulty on understanding where to start and how to solve the problem. Any help will be appreciated. Below is the question:
1) An object of massM is projected vertically upwards from the surface of the Earth. It experiences air resistance which is proportional to the square of the magnitude of its velocity. Newton's equation of motion in this case is
dv/dt= -g - (B(beta)/M)/v^2
where B (beta)> 0 is the strength of the air resistance and g > 0 is the local gravitational constant.
a) Seperate variables in equation (1) and substitute
u = v(Square root)(B(beta)/Mg)
to obtain an expression for the upward velocity functionv(t), with initialcondition v(0) = v0.
b) Use your answer to the previous part of this question to obtain the verticalheight function,y(t), giving the height of the object at time t, assume theinitial condition is y(0) = h.
c) Now perform a similar analysis for the case when the object is projecteddownwards to nd that the height functiony(t) is given the expression
y(t) = y0 - M/k log (cosh (A-t)(Square root)(kg/M))/cosh(B)
whereA;B are constants (what is y0?). If the initial velocity is zero, describe the downward velocity as t -> infiniti.