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

Question

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

kj4uts · Answer

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kj4uts · Answer

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

irishboy123 · Answer

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

kj4uts · Answer

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

irishboy123 · Answer

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

kj4uts · Answer

39.2/2^2 = 9.8

irishboy123 · Answer

yeah

irishboy123 · Answer

what is X?

irishboy123 · Answer

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

irishboy123 · Answer

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

kj4uts · Answer

@IrishBoy123 120.05

irishboy123 · Answer

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