A stone is thrown straight up from the roof of an 48-ft building.The distance (in feet) of the stone from the ground at any time t (in seconds) is given by . Sketch the graph of h.When is the stone rising, and when is it falling? If the stone were to miss the building, when would it hit the ground?
A) Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3sec
B) Rising in the time interval (3, -1); falling in the time interval (-1, 1); when t = 1sec
C) Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3sec

Question

A stone is thrown straight up from the roof of an 48-ft building.The distance (in feet) of the stone from the ground at any time t (in seconds) is given by  . Sketch the graph of h.When is the stone rising, and when is it falling? If the stone were to miss the building, when would it hit the ground?
A) Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3sec 
B) Rising in the time interval (3, -1); falling in the time interval (-1, 1); when t = 1sec 
C) Rising in the time interval (0, 1); falling in the time interval (1, 3); when t = 3sec

Quizplus · Accepted Answer

The given function is h(t) = -16t^2 + 64t + 48. To determine when the stone is rising or falling, we need to look at the sign of its velocity which is the derivative of the height function h(t). Taking the first derivative of h(t), we get h'(t) = -32t + 64 For the stone to be rising, h'(t) > 0 -32t + 64 > 0 t < 2 For the stone to be falling, h'(t) < 0 -32t + 64 < 0 t > 2 Therefore, the stone is rising from 0 to 2 seconds, and falling from 2 to 3 seconds. The stone will hit the ground at t = 3 seconds. Option A is the only one that correctly identifies the time intervals when the stone is rising and falling, and also gives the correct time when it hits the ground.

A Stone Is Thrown Straight Up from the Roof of an 48-Ft