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

For this case we have:
"the distance it falls is directly proportional to the square of the time it has failed"
Thus,
d = k * t ^ 2
We search for k by means of the following statement:
"A ball is dropped over the edge of a vertical cliff and falls 39.2 meters in two seconds"
Thus,
k = d / (t ^ 2)
Substituting values:
k = 39.2 / (2 ^ 2)
k = 9.8
Substituting we have that the equation is:
d = 9.8 * t ^ 2
The distance for t = 3.5 is:
d = 9.8 * (3.5) ^ 2
d = 120.05 m
Answer:
The ball would have dropped 120.05 meters