help with physics homework?
A helicopter is ascending vertically with a speed of 5.20 m/sec. At a height of 125 meters above the earth, a package is dropped from a window. How much time will the package reach the ground?
Favorite Answer
The package has an initial velocity of +5.2m/s and an initial height of +125m (assuming the ground is 0m). We know the acceleration will be that of gravity (-9.81m/s^2). We can therefore use the following equation to find the velocity when it hits the ground:
vf^2 = vi^2 + 2ad
vf^2 = (5.2)^2 + 2(-9.81)(0 – 125)
vf = -49.79m/s
(the negative sign just indicates the downward direction)
Now we find the time using the following equation:
vf = vi + at
-49.79 = 5.2 + (-9.81)t
t = 5.61s
125 = -5.20t +0.5gt^2
125 = -5.2t + (0.5*9.8)t^2
125=-5.2t + 4.9t^2
0=-125 – 5.2t + 4.9t^2
t = (-b+/-sqrt(b^2-4ac) )/2a
t = (5.2+/-sqrt(5.2^2 – 4(4.9)(-125)) )/(2(4.9))
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