Question

The equation of projectile is y = ax - bx2 . its horizontal range is?

Answer 1

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 2

Answer: Range,
`R =(a)/(b)`

Step-by-step explanation:

The equation of trajectory is:

`y = x tan \theta (1-(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-(b)/(a)x)`

On comparing:

`tan \theta = a`

`R = (a)/(b)`

Hence, the horizontal range is
`R =(a)/(b)`