SOLUTION: A pair of skydivers jump out of an airplane 5.5 km. above the ground. The equation H=5500-5t(square)is an approximate model for divers' altitude in meters at t seconds after jumpin

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A pair of skydivers jump out of an airplane 5.5 km. above the ground. The equation H=5500-5t(square)is an approximate model for divers' altitude in meters at t seconds after jumpin      Log On


   

Question 109473: A pair of skydivers jump out of an airplane 5.5 km. above the ground. The equation H=5500-5t(square)is an approximate model for divers' altitude in meters at t seconds after jumping out of the plane.
If a parachute does not open at 1000m, how much time is left to use the emergency chute?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
You are given that the equation for the height above ground t seconds after jumping from
the plane is:
.
H+=+5500+-5t%5E2
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where H is the height t seconds after jumping out:
.
So let's find out how much time it would take for the skydivers to fall the entire distance
from the plane to the ground. When the divers reach the ground their height above ground is
zero feet. In this case, the time it takes to fall that far is:
.
0+=+5500+-+5t%5E2
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Solve this equation by subtracting 5500 from both sides to make the equation become:
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-5500+=+-5t%5E2
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Then divide both sides by -5 to get that:
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1100+=+t%5E2
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Finally, solve for t by taking the square root of both sides and you get:
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t+=+sqrt%281100%29+=+33.166
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So the time it takes to fall the 5500 feet from the plane to the ground is 33.166 seconds.
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But the time that it takes to fall from the plane to the 1000 ft level takes up some of
that 33.166 seconds. You can solve for that time by substituting 1000 into the height equation
to get:
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1000+=+5500+-+5t%5E2
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Subtract 5500 from both sides to get rid of the 5500 on the right side and you have:
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-4500+=+-5t%5E2
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Divide both sides of the equation by -5 to get:
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900+=+t%5E2
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and solve for t by taking the square root of both sides:
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30+=+t
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So if a skydiver jumps from a plane at 5500 feet and falls for 30 seconds he or she is at
the 1000 ft level. Since that skydiver will hit the ground in a total of 33.166 seconds after
the jump, there are only 3.166 seconds left to slow the descent (33.166 seconds for the entire
fall less the 30 seconds that the skydiver fell to get from 5500 feet to 1000 feet).
.
The answer to your problem is 3.166 seconds.
.
Hope this helps you to understand the problem a little better.
.