Final answer:
To determine the height of the building, we can use the equation h = (1/2) * g * t^2, where h is the height, g is the acceleration due to gravity, and t is the time taken to hit the ground. Given that the speed of the object when it hits the ground is 31 m/s, we can calculate the time taken to hit the ground as 3.163 seconds. Substituting this value into the equation, we find that the height of the building is approximately 48.7 meters.
Step-by-step explanation:
To determine the height of the building, we can use the equation for calculating the height of an object dropped from rest:
h = (1/2) * g * t^2
where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time taken to hit the ground. Rearranging the equation, we have:
h = (1/2) * g * t^2
t = sqrt(2h / g)
Given that the speed of the object when it hits the ground is 31 m/s, we can use the fact that the final velocity of a falling object is given by:
v = g * t
Rearranging the equation, we have:
t = v / g
Substituting the given values, we can calculate the time taken to hit the ground:
t = 31 / 9.8 = 3.163 s
Now, we can substitute this value of time into the equation for height to find the height of the building:
h = (1/2) * 9.8 * (3.163)^2 = 48.66 m
Therefore, the height of the building is approximately 48.7 meters.