the distance that a body falls through when dropped from a certain height varies directly with the square of the time of fall. A body falls through a total of 500m in 10 seconds. find the distance it falls through, in 9th second (in m)
Please help me solve this
Let g = 10 m/s^2.
d = 0.5g*t^2 = 5*9^2 = 405 m.
To solve this problem, we can use the concept of direct variation.
We are given that the distance a body falls is directly proportional to the square of the time of fall. Mathematically, we can represent this relationship as:
distance ∝ (time)^2
We can introduce a constant of proportionality, which we'll call k, to form the equation:
distance = k * (time)^2
Now, let's use the given information to find the constant of proportionality, k. We know that when the body falls for 10 seconds, it covers a distance of 500 meters. Substituting these values into the equation, we get:
500 = k * (10)^2
Simplifying this equation, we have:
500 = 100k
Dividing both sides by 100, we find:
k = 5
Now that we have determined the constant of proportionality, we can use it to find the distance the body falls through in the 9th second. Plugging in the values into the equation, we have:
distance = 5 * (9)^2
Simplifying this equation, we get:
distance = 5 * 81
distance = 405 meters
Therefore, the distance the body falls through in the 9th second is 405 meters.