Question

The formula for the height of a falling object is h = -4.9t^2 + k, where h is the height of the object in meters, t is the time in seconds, and k is the height, in meters, from which the object began its fall. If a rock is dropped from a building that is 200 meters tall, what is the height of the rock 2 seconds after it was dropped?

A. 192.2 meters
B. 184.6 meters
C. 180 meters
D. 172 meters

Answer 1

After 2 seconds, the rock falls to a height of approximately 180.4 meters, which we round to the nearest whole number, 180 meters, making the correct answer C. 180 meters.

Step-by-step explanation:

The question concerns the height of a rock that has been dropped from a building 200 meters tall after a fall time of 2 seconds. Using the provided formula for the height of a falling object, h = -4.9t^2 + k, where t is the time in seconds, and k is the initial height, we can calculate the height of the rock after 2 seconds. Given t = 2 and k = 200 meters, we substitute these values into the formula to get h = -4.9(2)^2 + 200 which simplifies to h = -4.9(4) + 200 resulting in h = -19.6 + 200, ultimately calculating a height of 180.4 meters. This result was not given as one of the options, so we should assume the question meant to round to the nearest whole number, making the correct answer C. 180 meters.