Sagot :
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
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, [tex]R =\frac{a}{b}[/tex]
Explanation:
The equation of trajectory is:
[tex]y = x tan \theta (1-\frac{x}{R})[/tex]
Where, [tex]\theta[/tex] is the angle of projectile, R is the horizontal range.
The equation of projectile is:
y = ax-bx²
[tex]\Rightarrow y = ax(1-\frac{b}{a}x)[/tex]
On comparing:
[tex]tan \theta = a[/tex]
[tex]R = \frac{a}{b}[/tex]
Hence, the horizontal range is [tex]R =\frac{a}{b}[/tex]