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°, 45° and 60°, respectively with the horizontally. Which of the following statements is correct?

A
A, B and C have unequal ranges.
B
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

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

Explanation:

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°.

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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