Question

A bottle dropped from a ballon reaches the ground in 20 seconds. Determine the height of the ballon if rest the air and a) It was at rest in the air and b)

It was ascending with a speed of 50 m/s when the bottle was dropped.​

Answer 1

The height of the balloon at rest is 1960 m above the ground. If the balloon was ascending at a speed of 50 m/s, the height is 960 m above the ground.

Step-by-step explanation:

Calculating the Height of the Balloon

To answer the student's two-part question, we will apply the principles of kinematics.

The acceleration due to gravity (g) is 9.8 m/s2, and we will assume that air resistance is negligible.

Part a: Balloon at Rest

The bottle is dropped from rest, so its initial velocity is 0 m/s.

The formula to calculate the height (h) in such a scenario is h = (gt2)/2, where t is the time taken to reach the ground. Plugging the values in, we get:

h = (9.8 m/s2 × (20 s)2) / 2

= 1960 m

Part b: Balloon Ascending at 50 m/s

Since the bottle is dropped from an ascending balloon, its initial velocity (u) will be -50 m/s (negative because the motion is in the opposite direction to gravity).

Using the formula h = ut + (gt2)/2, we calculate:

h = -50 m/s × 20 s + (9.8 m/s2 × (20 s)2) / 2

= -1000 m + 1960 m

= 960 m