## KJ4UTS one year ago If a ball is dropped near the surface of the earth, then the distance it falls is directly proportional to the square of the time it has fallen. A ball is dropped over the edge of a vertical cliff and falls 39.2 meters in two seconds. Determine the distance (in meters) the ball would have dropped in 3.5 seconds. The ball would have dropped ____ meters. Round your answer to two decimal places

1. KJ4UTS

2. KJ4UTS

Is this how you solve this problem 39.2 / 2 = 19.6 * 3.5 = 68.6

3. IrishBoy123

$x \propto t^2 \implies x = k t^2$ $\therefore k = \dfrac{x_1}{t_1^2} = \dfrac{x_2}{t_2^2}= \dfrac{x_3}{t_3^2} = \ldots$

4. KJ4UTS

I am a little confused by that what do I plug into where?

5. IrishBoy123

$\dfrac{39.2}{2^2} = \dfrac{X}{3.5^2}$

6. KJ4UTS

39.2/2^2 = 9.8

7. IrishBoy123

yeah

8. IrishBoy123

what is X?

9. IrishBoy123

? the distance it falls is directly proportional to **the square of** the time it has fallen more time, bigger drop, and its squared too.....

10. IrishBoy123

$\dfrac{39.2}{2^2} = \dfrac{X}{3.5^2}$ $X = 3.5^2 \cdot \dfrac{39.2}{2^2}$

11. KJ4UTS

@IrishBoy123 120.05

12. IrishBoy123

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