Object dropped from plane - where does it land?

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SUMMARY

The discussion centers on calculating the distance a plane must be from a target group when dropping an object from a height of 227 meters at a speed of 60 m/s. The initial calculations incorrectly used the equation for vertical motion, leading to confusion about the time of fall. The correct approach involves determining the time it takes for the object to fall using the equation \(227 m = \frac{1}{2} g t^2\), where \(g\) is the acceleration due to gravity (9.8 m/s²). The correct time of fall is approximately 6.77 seconds, resulting in a horizontal distance of 406.2 meters from the target.

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Homework Statement


A plane is dropping an object from a height of 227m, such that it lands at a group of people on the ground. The speed of the plane is 60 m/s. How many meters before the group does the plane have to drop the object such that it lands at their position?

Homework Equations


xf = xi + vix delta t + (1/2) ax(delta t)2

The Attempt at a Solution



From my understanding, I need to break up the x and y components of this problem. If I can find the time it takes the object to hit the ground, I can multiply it by the plane's velocity and see what distance the plane must be from the observers for the package to hit its target.

227 m = 9.8t m/s^2
(227 m)/(9.8 m/s^2) = t
t^2 = 23.162
t = sqrt(23.162)
t = 4.813 seconds

Now that I have the time it took for the object to fall, I can multiply it by the plane's velocity to see how far in the x direction the object will travel in 4.813 seconds:

4.813 s * 60 m/s = 288.78 m

This is the answer I get, but it isn't correct. I can't see how multiplying the velocity by the time is wrong, but perhaps I have the wrong time?

Thanks,
x^2
 
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x^2 said:
227 m = 9.8t m/s^2

Something is wrong with that equation, since the units are different on the 2 sides:

m ≠ s ⋅ m/s^2
m ≠ m/s
 

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