Question

A 1.0-kilogram ball is dropped from the roof of a building 40. meters tall. What is the approximate time of fall? [Neglect air resistance.]

Answer 1

2.856s Distance traveled under constant acceleration as a function of time is given by x=(gt^2)/2 where g is the acceleration and t is time. In this case acceleration is due to gravity and is 9.81m/s^2. The distance of interest is x=40m. Substituting and solving 40=(9.81*t^2 )/ 2 80 = 9.81*t^2 8.1549 = t^2 2.856s = t

Answer 2

H = 40 m, the height from which the ball is dropped.
m = 1 kg, the mass of the ball

Assume g = 9.8 m/s² and neglect air resistance.

The initial vertical velocity is zero.
If t = the time of flight, then
40 m = (1/2)*g*(t s)² = 0.5*9.8*t²
t² = 40/4.9 = 8.1633
t = 2.857 s

Answer:  2.9 s (nearest tenth)