How do I analyze and solve this problem?

Question

Allan is explaining the wonders of nature to his son. He and his son went to a roof top of a 120m-high building, then he threw a stone from the rooftop.

a. Neglecting the air friction, what is the acceleration of the stone due to gravity?

b. At what time will the stone fall to the ground?

c. With what velocity will a stone strike the ground if dropped from the top of a building?

Answer 1

acceleration due to gravity is -32 ft per second per second = -32 ft/sec^2

the equation for the stone's height is h(t) =-16t^2 + 120

it hits the ground when h(t) = 0 = -16t^2 + 120

16t^2 = 120

t^2 = 120/16 = 30/4

t = (1/2)sqr30 = about 2.74 seconds

acceleration = derivative of velocity

a = v'

velocity = integral of acceleration

v= integral of -16t^2 = -16t^3/3 = -40sqr30 = about -219.1 feet per second