a helicopter is ascending vertically with a speed of 5.20 m/s. at a height of 100 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: v0 for the package equals the speed of the helicopter). thank you !
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To find the time it takes for the package to reach the ground, we can use the equations of motion.
First, let's consider the motion of the package when it is dropped from the window. The initial velocity of the package, v0, is equal to the speed of the helicopter, which is 5.20 m/s. The final velocity, vf, when the package reaches the ground is 0 m/s since the package comes to rest on the ground.
Using the equation of motion: vf = v0 + at, where a is the acceleration and t is the time, we can rearrange the equation to solve for time.
In this case, the acceleration, a, would be the acceleration due to gravity, which is approximately -9.8 m/s^2. We use a negative sign because gravity accelerates objects downwards.
0 = 5.20 + (-9.8)t
Simplifying the equation, we have:
-9.8t = -5.20
Dividing both sides by -9.8, we get:
t = (-5.20) / (-9.8)
t ≈ 0.53 seconds
So, it will take approximately 0.53 seconds for the package to reach the ground.