A passenger in a helicopter traveling upwards at 23 m/s accidentally drops a package out the window. If it takes 16 seconds to reach the ground, how high to the nearest meter was the helicopter when the package was dropped?

See 2-23,7:55am post for solution.

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

h = ut + (1/2)gt^2

Where:
h = height
u = initial upward velocity (23 m/s)
g = acceleration due to gravity (-9.8 m/s^2, negative because it acts downwards)
t = time (16 seconds)

We want to find the height, so we need to plug in the values and solve the equation:

h = (23 m/s) * (16 s) + (1/2) * (-9.8 m/s^2) * (16 s)^2

Calculating this expression gives us:

h = 368 m + (-784 m)

Adding the two terms, we get:

h = -416 m

However, the negative sign indicates that the final height is below the initial height. Therefore, we take the absolute value, which gives us:

h = 416 m

Therefore, the helicopter was approximately 416 meters high when the package was dropped.