First slide

Projectile motion

Question

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 $h = A x - B x^{2}$ where h is height, x is horizontal distance, A and B are constants. The ratio A : B is $(g = 10 {ms}^{- 2})$

Moderate

A

1:5
B

5:1
C

1:40
D

40:1

Solution

Standard equation of projectile motion
$y = x \tan θ - \frac{g x^{2}}{2 u^{2} \cos^{2} θ}$
Comparing with given equation
$\begin{array}{l} A = \tan θ and B = \frac{g}{2 u^{2} \cos^{2} θ} \\ So \frac{A}{B} = \frac{\tan θ \times 2 u^{2} \cos^{2} θ}{g} = 40 \\ (As θ = 45^{\circ}, u = 20 m / s, g = 10 m / s^{2}) \end{array}$

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