The problem
A mobile game, Dash of Dylans, is modeling the launch of a projectile. The programmer determines, based on the distance in metres,
x, from the launch zone, the height, h, also in metres, will follow the quadratic given by h= -5(x2-110x).
At what distance from the launch zone will the projectile reach its maximum?
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Answer provided by our tutors
When the projectile is launched:
x =0 and h = 0
When the projectile also lands back to the earth also:
h = 0
Since, h= -5(x^2-110x) we need to find the non-zero solutions for the quadratic equation to know the maximum distance the projectile reached:
-5(x^2-110x) = 0
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Click here to see the step by step solution
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x = 110 m
The projectile will reach maximum hight at half distance (since the trajectory is parabolic), so the solution is:
110/2 = 55 m