Identify the initial conditions y(0) and y'(0) for the vertical motion of an object, if the object is dropped from a height of 45 feet. [Take the origin to be on the ground.]
A) y(0) = 0, y'(0) = 0
B) y(0) = 45, y'(0) = 45t
C) y(0) = 0, y'(0) = -45
D) y(0) = 45, y'(0) = 0

Question

Quizplus · Accepted Answer

The object is dropped from a height of 45 feet, so at the instant of dropping, the initial height is 45 feet above the ground level. Therefore, y(0) = 45. Initially, the object is at rest, so its initial velocity is 0. Therefore, y'(0) = 0. Hence, choice D is the correct option.

Identify the Initial Conditions Y(0) and Y'(0) for the Vertical