The height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.
What is the height?
The height is a vertical distance between two points. It is given that A model rocket is launched 25 feet from you. When the rocket is at height h, the distance d between you and the rocket is given by d = 625 + h² where h and d are measured in feet.
The height will be calculated by forming the two equations from the given data in the question.
25  =  625  +  h²
100  =  4  (  625  +  h² )
100  =  ( 2500  +  4h²  )
By solving both the equations:
100  -  25  =  2500  -  625  +  4h²  -  h²
3h²  =  1800
h  =  √600
h  =  24.49 feet
Therefore the height of the rocket when the distance between them is 10 feet will be h = 24.49 feet.
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