A body falling from a high tower travels 40m in the last 2.71 sec of its fall to ground. What is the height of the tower?
Answer please
To calculate the height of the tower, we need to use the equations of motion. The motion of a falling body can be described using the equation of motion:
h = (1/2) * g * t^2
Where:
h is the height of the tower
g is the acceleration due to gravity, approximately 9.8 m/s^2
t is the time taken to fall
Given that the body travels 40m in the last 2.71 seconds before hitting the ground, we can use this information to find the height of the tower.
First, we need to find the total time taken to fall from the tower. Since we know the body travels 40m in the last 2.71 seconds, we can assume that this time includes both the time the body travels 40m and the time for the rest of the fall. Let's denote the total time as T.
T - 2.71 = total time for the rest of the fall
Now, let's use this information to find the height of the tower.
h = (1/2) * g * (T - 2.71)^2
Substituting the known values, we get:
h = (1/2) * 9.8 * (T - 2.71)^2
To solve for h, we need to find the value of T. We can use another equation of motion for free fall:
h = (1/2) * g * T^2
Since the body falls from rest, we can set the initial velocity to zero. Rearranging the equation, we have:
T = sqrt(2h / g)
Substituting this equation into the previous equation, we get:
h = (1/2) * 9.8 * (sqrt(2h / g) - 2.71)^2
Now, we can solve this equation to find the height of the tower. However, it is not a simple algebraic equation and requires an iterative approach or numerical methods to find the value of h. Assuming you don't want to go through the numerical approach, we can use a scientific calculator or a software program such as Excel to solve this equation and find the value of h.