Two stones are projected with same speed but making different angles with horizontal. Their ranges a

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3-2.Motion in Plane

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Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\pi /3$ and its maximum height is $h_1$ then the maximum height of the other will be

$3h_1$

$2h_1$

$h_1/2$

$h_1/3$

Solution

$\frac{\mathrm{h}_{2}}{\mathrm{h}_{1}}=\frac{\mathrm{u}^{2} \sin ^{2} \theta_{2}}{2 \mathrm{g}} \times \frac{2 \mathrm{g}}{\mathrm{u}^{2} \sin ^{2} \theta_{1}}$

$=\frac{\sin ^{2} \theta_{2}}{\sin ^{2} \theta_{1}}=\frac{\sin ^{2} \pi / 6}{\sin ^{2} \pi / 3}=\frac{1}{3}$

$\therefore \quad \mathrm{h}_{2}=\mathrm{h}_{1} / 3$

Standard 11

Physics

Given below are two statements. One is labelled as Assertion $A$ and the other is labelled as Reason $R$.

Assertion A :Two identical balls $A$ and $B$ thrown with same velocity '$u$ ' at two different angles with horizontal attained the same range $R$. If $A$ and $B$ reached the maximum height $h_{1}$ and $h_{2}$ respectively, then $R =4 \sqrt{ h _{1} h _{2}}$

Reason R: Product of said heights.

$h _{1} h _{2}=\left(\frac{u^{2} \sin ^{2} \theta}{2 g }\right) \cdot\left(\frac{u^{2} \cos ^{2} \theta}{2 g }\right)$

Choose the $CORRECT$ answer

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(JEE MAIN-2022)

A projectile is thrown at an angle $\theta$ such that it is just able to cross a vertical wall at its highest point as shown in the figure.The angle $\theta$ at which the projectile is thrown is given by

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The trajectory of a projectile in a vertical plane is $y =\alpha x -\beta x ^{2},$ where $\alpha$ and $\beta$ are constants and $x \& y$ are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $H$ are respectively given by :-

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(JEE MAIN-2021)

Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta _1$ and $\theta_2$ respectively from the horizontal, then answer the following question

If $v_1\,\,cos\,\,\theta _1 = v_2\,\,cos\,\,\theta _2$, then choose the incorrect statement

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If $R$ and $H$ represent the horizontal range and the maximum height achieved by a projectile then which of the relation exists?

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(AIIMS-2009)

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\pi /3$ and its maximum height is $h_1$ then the maximum height of the other will be

Solution

Similar Questions

A projectile is thrown at an angle $\theta$ such that it is just able to cross a vertical wall at its highest point as shown in the figure.The angle $\theta$ at which the projectile is thrown is given by

If $R$ and $H$ represent the horizontal range and the maximum height achieved by a projectile then which of the relation exists?

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