An object is thrown upward with a velocity of 9.8 m/s from a stationary balloon that is 14.6 m 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 kinematic equation h=h0+vt-1/2at^2, where h is the final height (0 m), h0 is the initial height (14.6 m), v is the initial velocity (9.8 m/s), a is the acceleration (-9.8 m/s^2), and t is the time, we can solve for t:

0 = 14.6 + 9.8t - (1/2)(9.8)(t^2)
0 = 14.6 + 4.9t^2 - 4.9t^2
0 = 14.6

This is a non-physical solution, so we reject it. The other solution is:

t = (-9.8 ± sqrt(9.8^2 - 4(1/2)(-9.8)(14.6)))/(2(1/2)(-9.8))
t = (-9.8 ± sqrt(385.36))/(-9.8)
t = (19.6/9.8) or t = (-29.4/9.8)

We can discard the negative solution since time cannot be negative. Therefore, the time until the object impacts the ground is approximately 3.0 seconds. Thus, the correct answer is (C) 3.0 s.

An Object Is Thrown Upward with a Velocity of 9