TS EAMCET · Maths · Application of Derivatives
If a balloon lying at an altitude of 30 m from an observer at a particular instant is moving horizontally at the rate of \(1 \mathrm{~m} / \mathrm{s}\) away from him, then the rate at which the balloon is moving away directly from the observer at the \(40^{\text {th }}\) second is (in \(\mathrm{m} / \mathrm{s}\) )
- A \(1.2\)
- B \(0.9\)
- C \(0.6\)
- D \(0.8\)
Answer & Solution
Correct Answer
(D) \(0.8\)
Step-by-step Solution
Detailed explanation
\( x = 1 \, \mathrm{m/s} \times 40 \, \mathrm{s} = 40 \, \mathrm{m} \) \( z = \sqrt{x^2 + h^2} = \sqrt{40^2 + 30^2} = \sqrt{1600 + 900} = \sqrt{2500} = 50 \, \mathrm{m} \) \( \frac{dz}{dt} = \frac{x}{z} \frac{dx}{dt} = \frac{40}{50} \times 1 = 0.8 \, \mathrm{m/s} \)
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
- The domain and range of \(f(x)=\frac{1}{\sqrt{|x|-x^2}}\) are A and B respectively. Then \(\mathrm{A} \cup \mathrm{B}=\)TS EAMCET 2025 Medium
- The line among the following which touches the parabola \(y^2=4 a x\), isTS EAMCET 2005 Medium
- If \((1+x)^{15}=a_0+a_1 x+\ldots+a_{15} x^{15}, \quad\) then \(\sum_{r=1}^{15} r \frac{a_r}{a_r-1}\) is equal toTS EAMCET 2005 Hard
- The equation of lowest degree with rational coefficients having roots \(\sqrt{3}+\sqrt{2} i\) and \(\sqrt{3}-\sqrt{2}\) isTS EAMCET 2022 Medium
- If the curves \(x^2+p y^2=1\) and \(q x^2+y^2=1\) are orthogonal to each other, thenTS EAMCET 2013 Hard
- Match the points on the curve \(2 y^2=x+1\) with the slopes of normals at those points and choose the correct answer.
TS EAMCET 2004 Hard
More PYQs from TS EAMCET
- Let \(\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}\) be two non collinear vectors, \(\mathbf{O P}=x_1 \mathbf{a}+y_1 \mathbf{b}, \mathbf{O Q}=x_2 \mathbf{a}+y_2 \mathbf{b}\) and \(\mathbf{A}^{\prime} \mathbf{O}=\mathbf{O A}, \mathbf{B}^{\prime} \mathbf{O}=\mathbf{O B}\). If \(x_1=\frac{-3}{4}, x_2=\frac{1}{3}\), \(y_1=\frac{7}{4}, y_2=\frac{5}{3}\), thenTS EAMCET 2020 Easy
- An current is given by the expression, in amperes. The frequency and RMS value of the current respectively areTS EAMCET 2022 Easy
- If \(\frac{x^2+1}{\left(x^2+2\right)\left(x^2+3\right)}=\frac{\mathrm{A} x+\mathrm{B}}{x^2+2}+\frac{\mathrm{C} x+\mathrm{D}}{x^2+3}\), then \(\mathrm{A}+\mathrm{B}+\mathrm{C}+\mathrm{D}=\)TS EAMCET 2025 Easy
- In which of the following reactions the product is an ether?TS EAMCET 2005 Medium
- Common oxidation state of \(f\)-block elements is III. The other stable oxidation states of \({ }^{63} \mathrm{Eu}\) and \({ }^{65} \mathrm{~Tb}\) are respectivelyTS EAMCET 2019 Medium
- In a triangle \(\mathrm{ABC}\), if \(a=7, c=11, \cos \mathrm{A}=\frac{17}{22}, \cos \mathrm{C}=\frac{1}{14}\) then \(b \tan \frac{\mathrm{B}}{2} \tan \frac{\mathrm{C}-\mathrm{A}}{2}=\)TS EAMCET 2022 Medium