Suppose you throw an object from a great height, so that it reaches very nearly terminal velocity by time it hits the ground, By measuring the impact, you determine that this terminal velocity is -49 m/s.

a. Write the equation representing the velocity v(t) of the object at time t seconds given the initial velocity v0 and the fact that acceleration due to gravity is -9.8 m/s squared.

b. Determine the value of k, the "continuous percentage growth rate" from the velocity equation, by utilizing the information given concerning the terminal velocity.

c. Using the value of k you derived above, at what velocity must the object be thrown upward if you want it to reach its peak height after 3 sec?