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An object is projected with a velocity of 20 \mathrm{~m} / \mathrm{s} making an angle of  45^{\circ} with horizontal The equation for the trajectory is \mathrm{h=A x-B x^2} is height  \mathrm{x }  is horizontal distance, \mathrm{A}and \mathrm{B } are constant, the ratio \mathrm{A: B } is

Option: 1

1: 5


Option: 2

5: 1


Option: 3

1: 40


Option: 4

40: 1


Answers (1)

best_answer

standard Equation of trajectory is given by- 
\mathrm{y=x \tan \theta-\frac{g x^2}{2 u^2 \cos ^2 \theta}}...........(1)
Given trajectory,
\mathrm{y=A x-B x^2}..................................(2)
Compare (2) from (1) we get -
\mathrm{\begin{aligned} & A=\tan \theta \\ & B=\frac{g}{2 u^2 \cos ^2 \theta} \end{aligned}}
\mathrm{\begin{aligned} & \text { Ratio }\left(\frac{A}{B}\right)=\frac{\tan \theta}{\left[\frac{g}{2 u^2 \cos ^2 \theta}\right]} \\ & \frac{A}{B}=\frac{\tan \theta}{g} \times 2 u^2 \cos ^2 \theta \\ & \frac{A}{B}=\frac{\tan 45^{\circ}}{10} \times 2 \times(20)^2 \times \cos ^2 45^{\circ} \\ & \frac{A}{B}=\frac{1}{10} \times 2 \times 400 \times\left(\frac{1}{\sqrt{2}}\right)^2 \\ & \frac{A}{B}=80 \times \frac{1}{2}=\frac{40}{1} \\ & A: B=40: 1 \text { Ans. } \end{aligned}}

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himanshu.meshram

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