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.

Answer 1

it tells you the distance is proportional to the square of the time

so distance = kt^2
\[\frac{ d1 }{ d2 } =\frac{ t1^{2} }{ t2^{2} }\]

you know all except d2 - so solve for d2

Answer 2

So I plug in 32.9 and 2 (seconds) in?

Answer 3

in the first scenario d=32.9 and t=2
in the second scenario d is unknown and t= 3.5

put those 3 values into the equation to solve the unknown distance

Answer 4

32.9/2^2=k ?

Answer 5

Is that how I set the formula up because it would be 9.8 then?

Answer 6

@MrNood

Answer 7

32.9/3.5^2=3.2