A helicopter is ascending vertically with a speed of 5.20 m/s. At a height of 125 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground? [Hint: The package's initial speed equals the helicopter's.]

hf=Hi+vi*t-1/2 9.8 t^2

Hi=125
vi=5.2
hf=0
solve for t. Notice it is a quadratic equation, use the quadratic equation.

I am hopelessly lost and my physics class is a self-paced 100% online nightmare with no assistance available.

Ok, on this problem, do what I outlined.

Then I suggest a local tutor. There are a lot of smart kids around.

Given:

Vi=5.20m/s
h=125 m
g=9.8m/s²
Formula:
t=h-Vi ÷(over)½g
t=125m - 5.20m/s ÷(over) ½(9.8m/s²)
t=119.8s÷½(9.8s²)
t=119.8s÷4.9s²
t=24.45s
Explanation:
How did I get the answer 119.8s?
I subtracted 125 m and 5.20 m/s than cancelled out the meter.
How did I get the answer 4.9s²?
I divided 9.8m/s² by 2 simply getting it from the ½.
How I ended up with the answer 24.45s?
I simply cancelled out the second from the ² power of 4.9s² and cancelled out the s from 119.8s to have the answer.

To find the time it takes for the package to reach the ground, we need to determine how long it will take for the package to fall from a height of 125 m.

We know that the initial speed of the package is equal to the speed of the ascending helicopter, which is 5.20 m/s.

We can use the kinematic equation for free fall:

𝑑 = 𝑣₀𝑡 + 0.5𝑔𝑡²

In this equation:
- 𝑑 is the distance (125 m)
- 𝑣₀ is the initial speed (5.20 m/s)
- 𝑔 is the acceleration due to gravity (approximately 9.8 m/s²)
- 𝑡 is the time we're trying to find

Since the package is dropped, its initial speed is in the downward direction, opposite to the ascending helicopter. Therefore, we can use the negative sign for 𝑣₀.

Plugging in the values, we have:

125 = (-5.20)𝑡 + 0.5(9.8)𝑡²

Rearranging the equation, we get a quadratic equation:

0.5(9.8)𝑡² - 5.20𝑡 + 125 = 0

Now we can solve this equation to find the time it takes for the package to reach the ground.

Using the quadratic formula 𝑥 = (-𝑏 ± √(𝑏² - 4𝑎𝑐)) / (2𝑎), where 𝑎 = 0.5(9.8), 𝑏 = -5.20, and 𝑐 = 125, we can determine the values of 𝑡.

Calculating 𝑡, we find two solutions: 𝑡 = 10.20 s (ignoring the negative solution, as time cannot be negative).

Therefore, it takes approximately 10.20 seconds for the package to reach the ground.