Question

An object is projected with a velocity of 20 $m s^{- 1}$ making an angle of 45⁰ with horizontal. The equation for trajectory is h = Ax $-$ Bx² , where h is height, x is horizontal distance, A and B are constants. The ratio A : B is (Take, g = 10 $m s^{- 2}$ )

Moderate

Solution

Standard equation of projectile motion,
$y = x \tan θ - \frac{g x^{2}}{2 u^{2} \cos^{2} θ}$
Comparing with given equation,
$A = \tan θ and B = \frac{g}{2 u^{2} \cos^{2} θ}$
$So, \frac{A}{B} = \frac{\tan θ \times 2 u^{2} \cos^{2} θ}{g} = 40 : 1$
$(As θ = 45 °, u = 20 {ms}^{- 1}, g = 10 {ms}^{- 2})$

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