Answer:
a)
, b)
, c)
, d)
, e)
, f) 
Step-by-step explanation:
The velocity function can be derived by the differentiating the height function:

Velocities after 2 and 4 seconds are, respectively:
a) 
b) 
The maximum height is reached when velocity is zero. Then:

c) 
The maximum height is:
d) 
The time required to hit the ground is:

Roots of the second-order polynomial are:


Only the first root is physically reasonable.
e) 
The velocity when the projectile hits the ground is:
f) 
9240ft per second
(105mi/1hr * 5280ft/1mi * 1hr/60sec)
This is the concept of algebra, given that the elevator is 500ft above the ground and it is descending at a steady rate of 5ft/sec. Then height h, at time t of the elevator movement can be modeled by the equation:
h(t)=-5t+500.
The correct answer is h(t)=-5t+500