a body is falling downwards 48 meters in 4 seconds , calculate what distance would it fall in 9 seconds given that when a body falls distance varies as the square of time?
s = kt^2
so you want s such that
s/9^2 = 48/4^2
Given that the distance a body falls varies as the square of time, we can use the following formula:
distance = (initial speed * time) + (0.5 * acceleration * time^2)
In this case, the initial speed is 0 m/s (since the body is falling downwards), and the acceleration can be found by dividing the distance fallen by the square of the time.
Given:
Initial speed (u) = 0 m/s
Time (t1) = 4 s
Distance fallen (d1) = 48 m
First, we can calculate the acceleration:
acceleration (a) = (d1 - (u * t1)) / (0.5 * t1^2)
acceleration = (48 - (0 * 4)) / (0.5 * 4^2)
acceleration = (48 - 0) / (0.5 * 16)
acceleration = 48 / 8
acceleration = 6 m/s^2
Now, we can calculate the distance fallen in 9 seconds:
Time (t2) = 9 s
distance (d2) = (u * t2) + (0.5 * a * t2^2)
distance = (0 * 9) + (0.5 * 6 * 9^2)
distance = 0 + (0.5 * 6 * 81)
distance = 0 + 243
distance = 243 m
Therefore, the body would fall a distance of 243 meters in 9 seconds.
To calculate the distance the body would fall in 9 seconds, we need to use the relationship between distance and time. In this case, the distance is proportional to the square of time.
Let's denote the distance the body would fall in 9 seconds as D2.
According to the given information, we know that the distance the body falls in 4 seconds is 48 meters (D1 = 48 meters).
Using the relationship between distance and time (distance ∝ time^2), we can set up a proportion:
(D1 / D2) = (t1^2 / t2^2)
Substituting the given values:
(48 / D2) = (4^2 / 9^2)
Cross-multiplying the equation:
48 * 9^2 = 4^2 * D2
Simplifying the equation:
D2 = (48 * 81) / 16
Calculating the value of D2:
D2 = 243 meters
Therefore, the body would fall 243 meters in 9 seconds, based on the given information.