(C) The horizontal range $R$ of a projectile is given by $R = \frac{u^2 \sin(2\theta)}{g} = 90 \,m$.The maximum height $H$ is given by $H = \frac{u^2

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(C) The horizontal range $R$ of a projectile is given by $R = \frac{u^2 \sin(2\theta)}{g} = 90 \,m$.The maximum height $H$ is given by $H = \frac{u^2 \sin^2 \theta}{2g}$.Dividing $H$ by $R$:$\frac{H}{R} = \frac{u^2 \sin^2 \theta / 2g}{u^2 (2 \sin \theta \cos \theta) / g} = \frac{\tan \theta}{4}$.Given $\theta = 45^{\circ}$,$\tan 45^{\circ} = 1$.Therefore,$H = \frac{R \tan 45^{\circ}}{4} = \frac{90 \times 1}{4} = 22.5 \,m$.

Class 11 Physics 3-2.Motion in Plane Horizontal Projectile Motion

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In a sports competition,a javelin is thrown at an angle $45^{\circ}$,which recorded a range of $90 \,m$. The maximum height reached by the javelin is (Neglect air resistance and acceleration due to gravity $g = 10 \,ms^{-2}$)

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A
$45 \,m$
B
$30 \,m$
C
$22.5 \,m$
D
$30 \sqrt{2} \,m$

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3-2.Motion in Plane

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Horizontal Projectile Motion

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In a projectile motion,the velocity at maximum height is:

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Two projectiles are fired with the same initial speed from the same point on the ground at angles of $(45^{\circ}-\alpha)$ and $(45^{\circ}+\alpha)$,respectively,with the horizontal direction. The ratio of their maximum heights attained is:

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$A$ boy can throw a stone up to a maximum height of $10 \ m$. The maximum horizontal distance that the boy can throw the same stone up to will be .......... $m$.

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$A$ particle is projected horizontally from a tower with velocity $10\,m/s$. Taking $g=10\,m/s^2$,match the following two columns at time $t=1\,s$.
Column $I$ Column $II$
$(A)$ Horizontal component of velocity $(p)$ $5$ $SI$ unit
$(B)$ Vertical component of velocity $(q)$ $10$ $SI$ unit
$(C)$ Horizontal displacement $(r)$ $15$ $SI$ unit
$(D)$ Vertical displacement $(s)$ $20$ $SI$ unit

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$A$ ball is rolled off the edge of a horizontal table at a speed of $4\, m/s$. It hits the ground after $0.4\, s$. Which statement given below is true?

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Column $I$	Column $II$
$(A)$ Horizontal component of velocity	$(p)$ $5$ $SI$ unit
$(B)$ Vertical component of velocity	$(q)$ $10$ $SI$ unit
$(C)$ Horizontal displacement	$(r)$ $15$ $SI$ unit
$(D)$ Vertical displacement	$(s)$ $20$ $SI$ unit

In a sports competition,a javelin is thrown at an angle $45^{\circ}$,which recorded a range of $90 \,m$. The maximum height reached by the javelin is (Neglect air resistance and acceleration due to gravity $g = 10 \,ms^{-2}$)

Similar Questions

In a projectile motion,the velocity at maximum height is:

Two projectiles are fired with the same initial speed from the same point on the ground at angles of $(45^{\circ}-\alpha)$ and $(45^{\circ}+\alpha)$,respectively,with the horizontal direction. The ratio of their maximum heights attained is:

$A$ boy can throw a stone up to a maximum height of $10 \ m$. The maximum horizontal distance that the boy can throw the same stone up to will be .......... $m$.

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