Answer to Question #40767 in Differential Equations for wanianse tayeb

Question

An object of mass m kg of projected vertically upward from the gravity with initial velocity u ms-1. assumes that the forces acting on the object are the gravitational forces and the retarding force due to the air resistance with a magnitude of alpha modulus velocity where alpha is a positive constant and velocity is the object at time.
1. if the mass of the object is 0.1 kg, the initial velocity is 5 ms-1, alpha is 1.0 kg s-1, and g is 10 ms-1
a) calculate the time taken for the object to reach the highest point
b) estimate the time taken for the object to descend from the highest point in the ground
2. Repeat step 3 with a mass 0.1 kg, and various masses alpha between 0.02 kg s-1to 2.0 kgs-1. tabulate your results in an appropriate table.