An object is thrown upward with a velocity of 32 ft/s from a stationary balloon that is 48 ft above the ground. If air resistance is ignored, the total time until the object impacts the ground is
A) 1.0 s.
B) 2.0 s.
C) 3.0 s.
D) 4.0 s.
E) 6.0 s.

Question

Quizplus · Accepted Answer

Using the equation h = vt - 16t^2, where h is the height, v is the initial velocity, t is the time, and g is the acceleration due to gravity, we get:
48 = 32t - 16t^2
Simplifying and rearranging the equation, we get:
16t^2 - 32t + 48 = 0
Dividing both sides by 16, we get:
t^2 - 2t + 3 = 0
Factoring the equation, we get:
(t-1)(t-3) = 0
Therefore, t = 1 or t = 3. However, since the object is thrown upward and then falls back down, we know that it takes the same amount of time to reach its peak height as it does to fall back down to its starting point. Therefore, the total time until the object impacts the ground is 2t, which is 6 seconds. However, the question asks for the total time until the object impacts the ground, not the time until it reaches its peak height, so the correct answer is 3 seconds.

An Object Is Thrown Upward with a Velocity of 32