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,distances varies directly as the square of time.
(9/4)^2 * 48
No
To solve this problem, we can use the direct variation formula:
Distance = k * (Time^2)
We are given that the body falls 48 meters in 4 seconds. Therefore, we can use these values to find the value of k. Substituting the given values into the formula:
48 = k * (4^2)
48 = k * 16
k = 48 / 16
k = 3
Now that we have the value of k, we can find the distance the body would fall in 9 seconds by substituting the new time value:
Distance = 3 * (9^2)
Distance = 3 * 81
Distance = 243 meters
Therefore, the body would fall 243 meters in 9 seconds.
To calculate the distance a body would fall in 9 seconds, given that distances vary directly as the square of time, we need to find the constant of variation (k) first.
Given:
Distance (d_1) = 48 meters
Time (t_1) = 4 seconds
We can set up a proportion using the formula for direct variation:
d_1 / t_1^2 = d_2 / t_2^2
Plugging in the given values, we have:
48 / 4^2 = d_2 / 9^2
Solving for d_2 (the distance fallen in 9 seconds):
48 / 16 = d_2 / 81
Cross-multiplying, we get:
16 * d_2 = 48 * 81
d_2 = (48 * 81) / 16
Calculating this expression:
d_2 = 243 meters
Therefore, the body would fall a distance of 243 meters in 9 seconds.