The equation of a projectile is [tex]y = ax - bx^2[/tex]. What is its horizontal range?

y = a x - b x^2 Range is a/b
y = tan Ф x - g x² / 2 u² cos² Ф tan Ф = a - equation 1 b = g / 2u² cos² Ф so u² cos² Ф = g /2b - equation 2
R = u cos Ф * 2 * u sin Ф / g = 2/g sinФ u² cos Ф = 2 /g tan Ф u² cos² Ф by using equation 1 and equation 2 = (2 /g ) a (g / 2b ) = a / b

Answered by Everest2017 | 2024-06-10

The equation of trajectory is:
y = x t an θ ( 1 − R x ​ )
Where, θ is the angle of projectile, R is the horizontal range.
The equation of projectile is:
y = ax-bx²
⇒ y = a x ( 1 − a b ​ x )
On comparing:
t an θ = a
R = b a ​
Hence, the horizontal range is R = b a ​

Answered by ariston | 2024-06-11

The horizontal range of the projectile described by the equation y = a x − b x 2 is given by R = b a ​ . This formula is derived from analyzing the points at which the projectile returns to the same vertical level. The range is directly influenced by the coefficients a and b in the equation.
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Answered by ariston | 2024-12-24