An object was dropped from the top a tall building. During the last two seconds of the fall in traveled 80m.
A) Find the total time of the fall. Assume that the gravitational acceleration is a constant 10m/s and air resistance is negligible.
B) Calculate the height of the building.
To solve this problem, we can use the equation of motion for free fall:
d = v_i * t + (1/2) * a * t^2
Where:
d is the displacement (distance traveled)
v_i is the initial velocity (0 m/s since the object was dropped)
t is the time
a is the acceleration due to gravity (10 m/s^2)
A) Find the total time of the fall:
Given that the object traveled 80 m during the last two seconds of the fall, we can set up the equation as follows:
80 = 0 * 2 + (1/2) * 10 * 2^2
Using the equation, we can solve for the time (t):
80 = 0 + 10 * 2^2
80 = 0 + 40
t = √(80/10)
t ≈ 2.83 seconds
So, the total time of the fall is approximately 2.83 seconds.
B) Calculate the height of the building:
To find the height of the building, we can use the equation of motion with the total time (t) and the acceleration due to gravity (a):
d = 0 * t + (1/2) * 10 * t^2
Substituting the value of t:
d = 0 + (1/2) * 10 * (2.83^2)
d = (1/2) * 10 * 8
d = 40 * 8
d = 320 meters
Therefore, the height of the building is 320 meters.