Verified Answer :

Everest2017

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

Answer: Range, \(R =\frac{a}{b}\)

Explanation:

The equation of trajectory is:

\(y = x tan \theta (1-\frac{x}{R})\)

Where, \(\theta\) is the angle of projectile, R is the horizontal range.

The equation of projectile is:

y = ax-bx²

\(\Rightarrow y = ax(1-\frac{b}{a}x)\)

On comparing:

\(tan \theta = a\)

\(R = \frac{a}{b}\)

Hence, the horizontal range is \(R =\frac{a}{b}\)

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