An object is projected with a velocity of 20 m/s making an angle of 45 o with horizontal. The equation for the trajectory is h = Ax – Bx 2 where h is height, x is horizontal distance, A and B are constants. The ratio A : B is (g = 10 ms –2 )
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Standard equation of projectile motion
\(y = x \tan \theta - \frac{g x^{2}}{2 u^{2} \cos^{2} \theta}\)
Comparing with given equation
\(A = \tan \theta\) and \(B = \frac{g}{2 u^{2} \cos^{2} \theta}\)
So \(\frac{A}{B} = \frac{\tan \theta \times 2u^{2} \cos^{2} \theta}{g} = 40\)
(As \(\theta = 45^\circ, u = 20 \text{ m/s}, g = 10 \text{ m/s}^2\) )
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