Three particles A, B and C projected from the same point with the… - Vidyadip

MCQ

Three particles $A, B$ and $C $projected from the same point with the same initial speeds making angle $30^\circ , 45^\circ$ and $60^\circ ,$ respectively with the horizontally. Which of the following statements is correct?

A
$A, B$ and $C$ have unequal ranges.
✓
Ranges of $A$ and $C$ are less than that of $B.$
C
Ranges of $A$ and $C$ are equal and greater than that of $B.$
D
$A, B$ and $C$ have equal ranges.

✓

Answer

Correct option: B.

Ranges of $A$ and $C$ are less than that of $B.$

When a body is projected at an angle with the horizontal with initial velocity $u,$ then the horizontal range $R$ of projectile is $\text{R}=\frac{\text{u}^2\sin2\theta}{\text{g}}.$
Clearly, for maximum horizontal range $\sin2\theta=1$ or $2\theta=90^\circ$ or $\theta=45^\circ.$
Hence, in order to achieve maximum range, the body should be projected at $45^\circ .$
In this case $\text{R}_\text{max}=\frac{\text{u}^2}{\text{g}}$
Hence, ranges of $A$ and $C$ are less than that of $B.$

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