Question

2 a ball is thrown upwards from the top of a 600 foot building and reaches 664 feet before falling back down to the ground.

determine the position of and velocity function for the ball.
Determine the average velocity on the interval 1,3
Find the instantaneous velocity at 3
Find the time required for the ball to reach ground level.
Find the velocity of the ball at impact.

Answer 1

It went up 64 feet from the roof. What was its initial speed and how long to the top? g = 32 ft/s^2 approximately here on earth.
v = Vi - 32 t where t is time to top
at the top v = 0
so Vi = 32 t
so t = Vi/32
h = 664 at top
h = 600 + Vi t - (32/2) t^2
so 64 = Vi t - (32/2) t^2
64 = Vi^2/32 - (32/2) Vi^2/32^2
64 = 16 Vi^2
Vi = 8/4 = 2 ft/second
Now you have what you need to solve the whole problem
now let t = time from the throw
v = 2 - 32 t
h = 600 + 2 t - 16 t^2
solve quadratic for t at h = 0
then get v at h = 0 from 2-32 t