A rock is dropped from a height of 828.1 meters and falls toward earth in a straight line. In t seconds the rock drops a distance of 4.9t² meters. What is the instantaneous velocity downward when it hits the ground? A) 3,360,173.089 meters/s B) 127.4 meters/s C) 63.7 meters/s D) 9.8 meters/s E) 26 meters/s

Question

Quizplus · Accepted Answer

The formula for the instantaneous velocity of a falling object is given by v = sqrt(2gh), where g is the acceleration due to gravity and h is the height from which the object was dropped. In this problem, h = 828.1 meters. To find the time it takes for the rock to hit the ground, we set the distance fallen equal to the total height and solve for t: 828.1 = 4.9t^2, which gives t = sqrt(828.1/4.9) = 16.07 seconds. Thus, the final velocity of the rock is v = sqrt(2 * 9.8 * 828.1) = 126.98 meters/second, which is approximately equal to 127.4 meters/second (rounded to one decimal place). Therefore, the correct answer is B.

A Rock Is Dropped from a Height of 828