A passenger in a helicopter traveling upwards at 19 m/s accidentally drops a package out the window. If it takes 14 seconds to reach the ground, how high to the nearest meter was the helicopter when the package was dropped?

To the nearest meter what was the maximum height of the package above the ground in the previous problem?

Well, isn't this a high-flying question! Let's calculate some heights, shall we?

To find out how high the helicopter was when the package was dropped, we can use the equation:

h = v * t

where h is the height, v is the velocity, and t is the time. Plugging in the given values, we get:

h = 19 m/s * 14 s

That gives us a height of 266 meters. So, the helicopter was flying at a whopping 266 meters above the ground when the package took its leap of faith!

Now, to find the maximum height of the package, we need to use a different equation:

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

where g is the acceleration due to gravity. Now, I'd love to make a joke about gravity, but it's no laughing matter. So let's plug in the values and calculate:

h_max = (1/2) * 9.8 m/s^2 * (14 s)^2

Doing the math, the maximum height of the package above the ground is approximately 960 meters.

So, while the helicopter was hovering at a height of 266 meters, that daring package reached a maximum height of 960 meters! That's one adventurous package, I must say.

To find the height of the helicopter when the package was dropped, we can use the formula:

h = v*t + (1/2)*g*t^2

Where:
h = height
v = initial velocity (19 m/s, upwards in this case)
t = time (14 seconds)
g = acceleration due to gravity (9.8 m/s^2)

Substituting the given values into the formula:

h = 19 m/s * 14 s + (1/2) * 9.8 m/s^2 * (14 s)^2

Simplifying:

h = 266 m + 9.8 m/s^2 * 98 s^2

h = 266 m + 960.4 m

h = 1226.4 m

Therefore, the height of the helicopter when the package was dropped was approximately 1226 meters.

To find the maximum height of the package above the ground, we need to calculate the displacement of the package during its free fall. Since the package was dropped, its initial velocity is 0 m/s, and we need to find the maximum height (h_max).

Using the formula:

h = h_max + (1/2)g*t^2

Where:
h = height (0 m, as the package reaches the ground)
h_max = maximum height
g = acceleration due to gravity (9.8 m/s^2)
t = time (14 seconds)

Substituting the given values into the formula:

0 m = h_max + (1/2) * 9.8 m/s^2 * (14 s)^2

Simplifying:

0 m = h_max + 9.8 m/s^2 * 98 s^2

h_max = - 9.8 m/s^2 * 98 s^2

h_max = - 960.4 m

As height cannot be negative, the maximum height of the package above the ground is 0 meters.

To find the height of the helicopter when the package was dropped, we can use the equation of motion for an object in freefall. The equation is:

h = (1/2)gt^2

Where:
h is the height (in meters)
g is the acceleration due to gravity (approximately 9.8 m/s^2)
t is the time (in seconds)

Using the given information, we have:
Initial velocity of the package (vo) = 19 m/s
Time of flight (t) = 14 s

Now, let's calculate the height of the helicopter when the package was dropped:

h = (1/2)gt^2
h = (1/2)(9.8 m/s^2)(14 s)^2
h = (0.5)(9.8 m/s^2)(196 s^2)
h = 960.4 m

Therefore, the helicopter was approximately 960 meters above the ground when the package was dropped.

To find the maximum height of the package above the ground, we can use the equation for the height of an object in freefall:

h_max = vo^2 / (2g)

Using the given information, we have:
Initial velocity of the package (vo) = 0 m/s (since it was dropped)
Acceleration due to gravity (g) = 9.8 m/s^2

Now, let's calculate the maximum height of the package above the ground:

h_max = vo^2 / (2g)
h_max = 19^2 / (2 * 9.8)
h_max = 361 / 19.6
h_max ≈ 18.4 m

Therefore, the maximum height of the package above the ground is approximately 18 meters.

Height change after release

= 19 t - (g/2)t^2
= -H when t = 14 s.
H is the height above ground where it is released and g is the acceleration of gravity.

Solve for H.

266 - 960 = -H
H = 694 m

It rises a distance h above H before coming back down.
g h = V^2/2 where V is the initial upward speed. (From energy considerations)
h = 18.4 m

max height = 694 + 18 = 712 m