Question

Two identical balls $P$ and $Q$ are projected with same speeds in vertical plane from same point $O$ with making projection angles with horizontal ${30}^{\circ }$ and ${60}^{\circ }$, respectively and they fall directly on plane $AB$ at points $P^{\prime }$ and $Q^{\prime }$ respectively. Which of the following statement is true about distance as given in options?

• A. $A{P}^{\prime }>A{Q}^{\prime }$
• B. $A{P}^{\prime }<A{Q}^{\prime }$
• C. $A{P}^{\prime }\le A{Q}^{\prime }$
• D. As there are complimentary projection angles

Answer 1

Answer: (A)

$A{P}^{\prime }>A{Q}^{\prime }$

Given,
Projection angle of ball $P={30}^{\circ }$
Projection angle of ball $Q={60}^{\circ }$
According to the question,
For complimentary angles ranges, $ON$ is same for $P$ and $Q$ as $O$ and $N$ are on same horizontal plane.
From figure $A{P}^{\prime }>A{Q}^{\prime }$