(A) For maximum range,the angle of projection is $\theta = 45^\circ$. The range $R$ is given as $100\, km = 10^5\, m$.The formula for range is $R = \f

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(A) For maximum range,the angle of projection is $\theta = 45^\circ$. The range $R$ is given as $100\, km = 10^5\, m$.The formula for range is $R = \frac{u^2 \sin(2\theta)}{g}$. Since $\sin(90^\circ) = 1$,we have $R = \frac{u^2}{g}$,so $u^2 = Rg$.The formula for maximum height is $H = \frac{u^2 \sin^2 \theta}{2g}$.Substituting $u^2 = Rg$ and $\theta = 45^\circ$ $(\sin^2 45^\circ = 1/2)$:$H = \frac{(Rg) \times (1/2)}{2g} = \frac{R}{4}$.Given $R = 10^5\, m$,we get $H = \frac{10^5}{4} = 2.5 \times 10^4\, m$.

Class 11 Physics 2 Motion in a Plane Horizontal Projectile Motion

Medium

$A$ missile is fired for maximum range at your town from a place $100\, km$ away from you. If the missile is fired for maximum range,what is the maximum height reached by the missile? (Take $g = 10\, m/s^2$)

A
$2.5\times10^4\, m$
B
$5.0\times10^4\, m$
C
$7.5\times10^4\, m$
D
$10^5\, m$

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2 Motion in a Plane

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Horizontal Projectile Motion

At what angle should a particle be projected to cover the maximum range (in $^{\circ}$)?

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$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \, m$. With the same effort,he throws the ball vertically upwards. The maximum height attained by the ball is ......... $m$.

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If the height of a projectile at a time of $2 \ s$ from the beginning of motion is $60 \ m$,then the time of flight of the projectile is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $s$)

MediumAP EAMCET 2025

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$A$ ball is projected with a velocity of $10 \ ms^{-1}$ at an angle of $60^{\circ}$ with the vertical direction. Its speed at the highest point of its trajectory will be $............... \ ms^{-1}$.

MediumNEET 2022

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$A$ body is projected into a vertical $X-Y$ plane with the $X$-axis along the horizontal and the $Y$-axis along the vertical with an initial velocity $(10 \hat{i} + p \hat{j}) \ m/s$. If the maximum height reached by the body is $50 \%$ of its range,then the value of $p$ is:

MediumAP EAMCET 2017

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$A$ missile is fired for maximum range at your town from a place $100\, km$ away from you. If the missile is fired for maximum range,what is the maximum height reached by the missile? (Take $g = 10\, m/s^2$)

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At what angle should a particle be projected to cover the maximum range (in $^{\circ}$)?

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \, m$. With the same effort,he throws the ball vertically upwards. The maximum height attained by the ball is ......... $m$.

If the height of a projectile at a time of $2 \ s$ from the beginning of motion is $60 \ m$,then the time of flight of the projectile is (Acceleration due to gravity $= 10 \ m \ s^{-2}$) (in $s$)

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