A balloon is ascending at a rate of +4.00 m/s to a height of 11.0 m above the ground when a package is dropped. In the absence of air resistance, the velocity of the ball when it hits the ground is
A) +15.2 m/s,
B) -15.2 m/s.
C) +14.7 m/s.
D) -14.7 m/s.
E) 0 m/s.

Question

Quizplus · Accepted Answer

When the package is dropped, its initial velocity is the same as the balloon's, which is +4.00 m/s. The package then falls freely under the effect of gravity, which accelerates it downwards at 9.81 m/s². After falling for a time t, the package hits the ground with a velocity v. Using the kinematic equation y = y0 + v0t + ½at², we can solve for t, which is the time it takes for the package to fall from a height of 11.0 m:

11.0 m = 0 + (4.00 m/s)t + ½(9.81 m/s²)t²
11.0 m = 4.90t² + 4.00t
0 = 4.90t² + 4.00t - 11.0
Using the quadratic formula, we get:
t = 1.21 s (ignoring the negative solution)
Therefore, the velocity of the package just before hitting the ground is:
v = v0 + at = 4.00 m/s + (9.81 m/s²)(1.21 s) = 15.2 m/s
The negative sign indicates that the velocity is in the opposite direction of the positive direction (upwards) we defined earlier, so the correct answer is B, -15.2 m/s.

A Balloon Is Ascending at a Rate of +4