The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are ${R}_{1}, {R}_{2}$ and ${H}_{1}$, ${H}_{2}$ respectively. Choose the correct option:
The ranges and heights for two projectiles projected with the same initial velocity at angles $42^{\circ}$ and $48^{\circ}$ with the horizontal are ${R}_{1}, {R}_{2}$ and ${H}_{1}$, ${H}_{2}$ respectively. Choose the correct option:
- [JEE MAIN 2021]
- A
${R}_{1}>{R}_{2}$ and ${H}_{1}={H}_{2}$
- B
${R}_{1}={R}_{2}$ and ${H}_{1}<{H}_{2}$
- C
${R}_{1}<{R}_{2}$ and ${H}_{1}<{H}_{2}$
- D
${R}_{1}={R}_{2}$ and ${H}_{1}={H}_{2}$
Similar Questions
Match the columns
Column $-I$
$R/H_{max}$
Column $-II$
Angle of projection $\theta $
$A.$ $1$
$1.$ ${60^o}$
$B.$ $4$
$2.$ ${30^o}$
$C.$ $4\sqrt 3$
$3.$ ${45^o}$
$D.$ $\frac {4}{\sqrt 3}$
$4.$ $tan^{-1}\,4\,=\,{76^o}$
Match the columns
| Column $-I$ $R/H_{max}$ |
Column $-II$ Angle of projection $\theta $ |
| $A.$ $1$ | $1.$ ${60^o}$ |
| $B.$ $4$ | $2.$ ${30^o}$ |
| $C.$ $4\sqrt 3$ | $3.$ ${45^o}$ |
| $D.$ $\frac {4}{\sqrt 3}$ | $4.$ $tan^{-1}\,4\,=\,{76^o}$ |
A projectile is thrown with a velocity of $50\,\, ms^{^{-1}}$ at an angle of $53^o$ with the horizontal .Choose the incorrect statement
A projectile is thrown with a velocity of $50\,\, ms^{^{-1}}$ at an angle of $53^o$ with the horizontal .Choose the incorrect statement
A bullet fired at an angle of $30^o$ with the horizontal hits the ground $3.0\; km$ away. By adjusting its angle of projection, can one hope to hit a target $5.0\; km$ away ? Assume the muzzle speed to be fixed, and neglect air resistance.
A bullet fired at an angle of $30^o$ with the horizontal hits the ground $3.0\; km$ away. By adjusting its angle of projection, can one hope to hit a target $5.0\; km$ away ? Assume the muzzle speed to be fixed, and neglect air resistance.
A particle is projected in air at some angle to the horizontal, moves along parabola as shown in figure where $x$ and $y$ indicate horizontal and vertical directions respectively. Shown in the diagram, direction of velocity and acceleration at points $A, \,B$ and $C$.
A particle is projected in air at some angle to the horizontal, moves along parabola as shown in figure where $x$ and $y$ indicate horizontal and vertical directions respectively. Shown in the diagram, direction of velocity and acceleration at points $A, \,B$ and $C$.
Galileo, in his book Two new sciences, stated that “for elevations which exceed or fall short of $45^o$ by equal amounts, the ranges are equal”. Prove this statement.
Galileo, in his book Two new sciences, stated that “for elevations which exceed or fall short of $45^o$ by equal amounts, the ranges are equal”. Prove this statement.