A helicopter is ascending vertically with a speed of 4.00 m/s. At a height of 185 m above the Earth, a package is dropped from a window. How much time does it take for the package to reach the ground?
To find the time it takes for the package to reach the ground, we can use the equation of motion for vertical motion. The equation is:
h = ut + (1/2)gt^2
Where:
h = height (in meters)
u = initial velocity (in meters per second)
t = time (in seconds)
g = acceleration due to gravity (approximately 9.8 m/s^2)
In this problem, the package is dropped from rest (u = 0), and the acceleration due to gravity is negative since it acts in the opposite direction of the ascent of the helicopter.
So, let's solve the equation for time (t):
185 = 0*t + (1/2)(-9.8)t^2
To simplify the equation, we can multiply both sides by 2:
370 = -9.8t^2
Now, divide both sides by -9.8:
t^2 = 370 / -9.8
t^2 = -37.76
Since time cannot be negative, we discard the negative solution and are left with:
t = √37.76 ≈ 6.146 seconds
Therefore, it takes approximately 6.146 seconds for the package to reach the ground when dropped from a height of 185 meters.