Question

A helicopter is ascending vertically with a speed of 1.00 m/s. At a height of 75 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]

(I accidentally closed the first thread of this question ugh)

Answer 1

s = distance = 75 + v t - (1/2) g (t)^2

find t for s = 0, the ground.
v = initial velocity, 1 m/s
g = 9.8 m/s^2

Answer 2

so what i have is

-75m = t + 4.9m/s^2 * t^2

that's the part where i get stuck.

to get there i put

0 = 75m + t - 1/2(-9.8m/s^2)t^

so what do i do from there?

Answer 3

With an equation of the type 0 = a t^2 + b t + c, a quadratic

the solutions are t = [-b +- sqrt(b^2 - 4 a c)]/ 2 a

often only one of the two solutions makes physical sense.

Answer 4

i'm sorry, i'm having some trouble understanding :/ Can you tell me what a, b, and c equal? In my physics class, we never bring in the quadratic formula, so it's hard for me to see what exactly you're doing.

Answer 5

The package is dropped at point A (75m from ground) and will go upwards with initial speed of 1 m/s until it reach the highest point B. Then, it returns (free fall) to the initial point (now point C) and continue until it hit the ground (point D). Then:

The time it need to reach the highest point (B) is:
\[t_{AB} = \frac{ v - v _0}{ g } = \frac {0-1}{-9.8} = 0.1s\]
Now, we consider the time from point B (highest point) and point C (at the same level of point A):
\[t_{BC} = t_{ABC}\]
Then:
\[t_{BC} ={ 0.1s}\]
Now the last stage of the trip: From C to D (ground level). Note that the package will have the same speed it had initially but in the opposite direction: \[t_{CD} = t\]\[h = v_0 + \frac{ 1 }{ 2 }g t^{2}\]\[75 = t + \frac{ 1 }{ 2 } 9.8 t^{2}\]
Where:
\[t_{CD} ={ 3.8s}\]
Finally, total time is:
\[T = t_{AB} + t_{BC} + t_{CD} = 0.1 + 0.1 + 3.8 \]
\[T = 4 s \]

Answer 6

a,b,c meant the factors you get when you put the equation into the form

0 = a t^2 + b t + c

other approach to solution seems clearer, though.

Answer 7

I'm glad I could help. Thanks for the medals (Douglas and Lainey). :)