JEE Mains · Maths · STD 11 - Trigonometrical equations
A man is observing, from the top of a tower, a boat speeding towards the tower from a certain point A, with uniform speed. At that point, angle of depression of the boat with the man's eye is \(30^{\circ}\) (Ignore man's height). After sailing for \(20\) seconds, towards the base of the tower (which is at the level of water), the boat has reached a point \(B\), where the angle of depression is \(45^{\circ}\). Then the time taken (in seconds) by the boat from \(B\) to reach the base of the tower is
- A \(10\)
- B \(10 \sqrt{3}\)
- C \(10(\sqrt{3}+1)\)
- D \(10(\sqrt{3}-1)\)
Answer & Solution
Correct Answer
(C) \(10(\sqrt{3}+1)\)
Step-by-step Solution
Detailed explanation
Let speed of boat is \(u m / s\) and height of tower is \(h\) meter \(\&\) distance \(AB = x\) metre \(\therefore x=h \cot 30^{\circ}-h \cot 45^{\circ}\) \(\Rightarrow x=h(\sqrt{3}-1)\) \(\therefore u =\frac{ x }{20}=\frac{ h (\sqrt{3}-1)}{20} m / s\) \(\therefore\) Time taken…
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 mean of the data set comprising of \(16\) observations is \(16.\) If one of the observation valued \(16\) is deleted and three new observations valued \(3, 4\) and \(5\) are added to the data, then the mean of the resultant data, is:JEE Mains 2015 Medium
- Let the tangent to the circle \(C _{1}: x^{2}+y^{2}=2\) at the point \(M (-1,1)\) intersect the circle \(C _{2}\) : \(( x -3)^{2}+(y-2)^{2}=5\), at two distinct points \(A\) and \(B\). If the tangents to \(C _{2}\) at the points \(A\) and \(B\) intersect at \(N\), then the area of the triangle \(ANB\) is equal toJEE Mains 2022 Hard
- Let \(\alpha, \beta\) be two roots of the equation \(x^{2}+(20)^{\frac{1}{4}} x+(5)^{\frac{1}{2}}=0\). Then \(\alpha^{8}+\beta^{8}\) is equal to:JEE Mains 2021 Easy
- The equations of two sides \(\mathrm{AB}\) and \(\mathrm{AC}\) of a triangle \(\mathrm{ABC}\) are \(4 \mathrm{x}+\mathrm{y}=14\) and \(3 \mathrm{x}-2 \mathrm{y}=5\), respectively. The point \(\left(2,-\frac{4}{3}\right)\) divides the third side \(\mathrm{BC}\) internally in the ratio \(2: 1\). The equation of the side \(\mathrm{BC}\) is :JEE Mains 2024 Hard
- Let \(m\) and \(M\) be respectively the minimum and maximum values of \(\left|\begin{array}{ccc}\cos ^{2} x & 1+\sin ^{2} x & \sin 2 x \\ 1+\cos ^{2} x & \sin ^{2} x & \sin 2 x \\ \cos ^{2} x & \sin ^{2} x & 1+\sin 2 x\end{array}\right|\). Then the ordered pair \(( m , M )\) is equal toJEE Mains 2020 Hard
- Let \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) be a thrice differentiable function such that \(f(0)=0, f(1)=1, f(2)=-1, f(3)=2\) and \(f(4)=-2\). Then, the minimum number of zeros of \(\left(3 f^{\prime} f^{\prime \prime}+f f^{\prime \prime \prime}\right)(x)\) is ...........JEE Mains 2024 Hard
More PYQs from JEE Mains
- From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :JEE Mains 2025 Hard
- If for some positive integer \(n,\) the coefficients of three consecutive terms in the binomial expansion of \((1+x)^{n+5}\) are in the ratio \(5: 10: 14,\) then the largest coefficient in this expansion isJEE Mains 2020 Hard
- Let \([x]\) denote the greatest integer less than or equal to \(x\). Then the domain of \(f(x)=\sec ^{-1}(2[x]+1)\) is :JEE Mains 2025 Easy
- Let \(z\) be a complex number such that \(\left|\frac{z-2 i}{z+i}\right|=2, z \neq-i\). Then \(z\) lies on the circle of radius \(2\) and centreJEE Mains 2023 Hard
- The value of \(4+\frac{1}{5+\frac{1}{4+\frac{1}{5+\frac{1}{4+\ldots \ldots \infty}}}}\) isJEE Mains 2021 Medium
- If the system of linear equations \(2 x+y-z=3\) \(x-y-z=\alpha\) \(3 x+3 y+\beta z=3\) has infinitely many solution, then \(\alpha+\beta-\alpha \beta\) is equal to .... .JEE Mains 2021 Medium