AP EAMCET · PHYSICS · Motion In Two Dimensions
The height of ceiling in an auditorium is 30 m. A ball is thrown with a speed of \(30 \mathrm{~m} \mathrm{~s}^{-1}\) from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the auditorium. Then the length of auditorium is
[Acceleration due to gravity \(=10 \mathrm{~m} \mathrm{~s}^{-2}\) ]
- A \(60 \sqrt{2} \mathrm{~m}\)
- B \(30 \sqrt{2} \mathrm{~m}\)
- C \(70 \sqrt{2} \mathrm{~m}\)
- D \(100 \sqrt{2} \mathrm{~m}\)
Answer & Solution
Correct Answer
(A) \(60 \sqrt{2} \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
\(h_{max} = \frac{u^2 \sin^2 \theta}{2g}\) \(30 = \frac{(30)^2 \sin^2 \theta}{2 \times 10} \Rightarrow \sin^2 \theta = \frac{30 \times 20}{900} = \frac{2}{3}\) \(\sin \theta = \sqrt{\frac{2}{3}}\)…
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