AP EAMCET · Maths · Heights and Distances
An aeroplane is flying at a constant speed, parallel to the horizontal ground at a height of 5 kms. A person on the ground observed that the angle of elevation of the plane is changed from \(15^{\circ}\) to \(30^{\circ}\) in the duration of 50 seconds, then the speed of the plane (in kmph) is
- A 100
- B 720
- C 360
- D 540
Answer & Solution
Correct Answer
(B) 720
Step-by-step Solution
Detailed explanation
\( D = h (\cot(\theta_1) - \cot(\theta_2)) = 5 (\cot(15^{\circ}) - \cot(30^{\circ})) \) \( D = 5 ((2+\sqrt{3}) - \sqrt{3}) = 5(2) = 10 \text{ km} \) \( \text{Speed} = \frac{D}{t} = \frac{10 \text{ km}}{50 \text{ s}} \times \frac{3600 \text{ s}}{1 \text{ h}} \)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Assertion (A) : If \(y=f(x)=(|x|-|x-1|)^2\), then \(\left(\frac{d y}{d x}\right)_{x=1}=1\)
Reason (R) : If \(\lim _{x \rightarrow a} \frac{f(x)-f(a)}{x-a}\) exist, then it is called derivative of \(\mathrm{f}(\mathrm{x})\) at \(\mathrm{x}=\mathrm{a}\).
ThenAP EAMCET 2025 Medium - Let \(u, v\) and \(w\) be non-coplanar vectors. Then the points corresponding to which of the following vectors are collinear.AP EAMCET 2020 Easy
- \(\int e^{x \operatorname{cosec} x} \cdot \operatorname{cosec} x \cdot(1-x \cot x) d x=\)AP EAMCET 2020 Easy
- For a hyberbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}=1\), if the length of the transvere axis is 8 and the distance between the foci is \(2 \sqrt{41}\), then the length of its latus rectum isAP EAMCET 2022 Easy
- If \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}\) and \(\mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\), then find the angle between the vectors \(2 \mathbf{a}+\mathbf{b}\) and \(\mathbf{a}+2 \mathbf{b}\).AP EAMCET 2020 Easy
- Observe the following statements :
\(\mathrm{A}: \int\left(\frac{x^2-1}{x^2}\right) e^{\frac{x^2+1}{x}} d x=e^{\frac{x^2+1}{x}}+c\)
\(\mathrm{R}: \int f^{\prime}(x) e^{f(x)} d x=f(x)+c\)
Then which of the following is true ?AP EAMCET 2006 Hard
More PYQs from AP EAMCET
- Identify the antioxidant used in foods.AP EAMCET 2016 Easy
- Given three vectors \(\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\), a vector in the plane of \(\mathbf{b}\) and \(\mathbf{c}\) whose projection on \(\mathbf{a}\) is of magnitude \(\sqrt{\frac{2}{3}}\) isAP EAMCET 2019 Medium
- A particle of mass \(4 m\) explodes into three pieces of masses \(m, m\) and \(2 \mathrm{~m}\). The equal masses move along \(X\)-axis and \(Y\)-axis with velocities \(4 \mathrm{~ms}^{-1}\) and \(6 \mathrm{~ms}^{-1}\) respectively. The magnitude of the velocity of the heavier mass isAP EAMCET 2009 Medium
- Let \(A\) be a square matrix of order 3 . Choose the correct option regarding the following statements
I. There exists a matrix \(B\) of order 3 such that \(A B=I_3\)
II. There exists a matrix \(C\) of order 3 such that \(C A=I_3\)
III. \(A\) is invertibleAP EAMCET 2020 Easy - If a real valued function \(f:[-1,2] \rightarrow B\) defined by
\(f(x)=\left\{\begin{array}{l}
1-x, \quad \text { when }-1 \leq x \leq 1 \\
x-1, \quad \text { when } 1 < x \leq 2
\end{array}\right.\)
is a surjection, then \(\mathrm{B}=\)AP EAMCET 2025 Medium - Integrating factor of the differential equation \(\sin x \frac{d y}{d x}-y \cos x=1\) isAP EAMCET 2024 Easy