A hot air balloon is traveling vertically upward

at a constant speed of 2.7 m/s. When
it is 11 m above the ground, a package is
released from the balloon.
After it is released, for how long is the
package in the air? The acceleration of gravity
is 9.8 m/s
2
.
Answer in units of s

To find the time for which the package is in the air, we need to calculate the time it takes for the package to fall to the ground from a height of 11 m.

First, let's calculate the time it would take for the package to fall to the ground without considering the upward speed of the balloon. We can use the equation of motion:

d = (1/2) * g * t^2

Where:
d is the distance traveled (11 m in this case),
g is the acceleration due to gravity (9.8 m/s^2),
t is the time taken.

Rearranging the equation to solve for time:

t^2 = (2 * d) / g

Substituting the values:

t^2 = (2 * 11) / 9.8
t^2 = 22 / 9.8
t^2 ≈ 2.24

Now, taking the square root of both sides to get the time:

t ≈ √2.24
t ≈ 1.497

Therefore, without considering the upward speed of the balloon, the package would take approximately 1.497 seconds to fall to the ground.

Since the balloon is traveling vertically upward at a constant speed of 2.7 m/s, the package will also be moving upward at this speed when it is released. So, the package will start at a speed of 2.7 m/s and gradually slow down due to the acceleration of gravity until it reaches a height of 0 m (the ground).

To find the time for which the package is in the air, we need to add the time it takes for the package to fall to the ground (1.497 seconds) to the time it takes for the package to reach a height of 0 m while moving upward at 2.7 m/s.

The time it takes for the package to reach a height of 0 m while moving upward can be calculated using the formula:

t = d / v

Where:
d is the distance traveled (11 m in this case),
v is the vertical velocity (2.7 m/s in this case),
t is the time taken.

Substituting the values:

t = 11 / 2.7
t ≈ 4.074

Now, adding the time it takes for the package to fall (1.497 seconds) and the time it takes to reach a height of 0 m while moving upward (4.074 seconds):

Total time in the air ≈ 1.497 + 4.074
Total time in the air ≈ 5.571 seconds

Therefore, the package will be in the air for approximately 5.571 seconds.

v0=2.7 (package was rising)

x0=11
x1=0
a=-9.8

x1=x0+v1*t+(1/2)at²
0=11+(2.7)t+(1/2)(-9.8)t²
Solve for t to get t=1.8 sec.