A body falling from a high tower travels 40 m in the last 2.71sec of its fall to the ground. What is the height of the tower?
To find the height of the tower, we need to use the equations of motion for a freely falling object.
The equation for the distance traveled by a falling object is given by:
d = ut + (1/2)gt^2
Where:
d = distance traveled
u = initial velocity (which is 0 as the object is dropped)
g = acceleration due to gravity (approximately 9.8 m/s^2)
t = time taken
From the problem, we are given that the object covers a distance of 40 m in the last 2.71 seconds of its fall. So we can write:
40 = (1/2) * 9.8 * (2.71)^2
We can solve this equation to find the time taken for the entire fall:
40 = 69.8434
This gives us a value of 69.8434 for the initial distance traveled. Now we can substitute this into the equation to find the total time of fall:
69.8434 = (1/2) * 9.8 * t^2
Simplifying:
9.8 * t^2 = 69.8434 * 2
t^2 = 14.4604653
t ≈ 3.805 seconds
Now, we can substitute the value of t into the equation for the height of the tower to find the answer:
d = ut + (1/2)gt^2
d = 0 * 3.805 + (1/2) * 9.8 * (3.805)^2
Simplifying:
d = 0 + (1/2) * 9.8 * 14.4604653
d ≈ 70.76 meters
Therefore, the height of the tower is approximately 70.76 meters.