KCET · Maths · Parabola
A stone is thrown vertically upwards from the top of a tower \(64 \mathrm{~m}\) high according to the law \(s=48 t-16 t^{2}\). The greatest height attained by the stone above ground is
- A \(36 \mathrm{~m}\)
- B \(32 \mathrm{~m}\)
- C \(100 \mathrm{~m}\)
- D \(64 \mathrm{~m}\)
Answer & Solution
Correct Answer
(C) \(100 \mathrm{~m}\)
Step-by-step Solution
Detailed explanation
Given, \(s=48 t-16 t^{2}\)
\(\Rightarrow \quad \frac{\mathrm{ds}}{\mathrm{dt}}=48-32 \mathrm{t}\)
At the greatest height, \(\mathrm{v}=\frac{\mathrm{ds}}{\mathrm{dt}}=0\)
\(\Rightarrow \quad 48-32 t=0\)
\(\Rightarrow \quad \mathrm{t}=\frac{3}{2}\)
\(\therefore \quad \mathrm{s}=48 \times \frac{3}{2}-16\left(\frac{3}{2}\right)^{2}\)
\(=36 \mathrm{~m}\)
\(\therefore\) Total height \(=64+36=100 \mathrm{~m}\)
\(\Rightarrow \quad \frac{\mathrm{ds}}{\mathrm{dt}}=48-32 \mathrm{t}\)
At the greatest height, \(\mathrm{v}=\frac{\mathrm{ds}}{\mathrm{dt}}=0\)
\(\Rightarrow \quad 48-32 t=0\)
\(\Rightarrow \quad \mathrm{t}=\frac{3}{2}\)
\(\therefore \quad \mathrm{s}=48 \times \frac{3}{2}-16\left(\frac{3}{2}\right)^{2}\)
\(=36 \mathrm{~m}\)
\(\therefore\) Total height \(=64+36=100 \mathrm{~m}\)
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
- If \( A=\left[\begin{array}{cc}3 & 1 \\ -1 & 2\end{array}\right] \) then \( A^{2}-5 A \) is equal toKCET 2016 Easy
- The value of \(\left|\begin{array}{ccc}1 & \log _{\mathrm{x}} \mathrm{y} & \log _{\mathrm{x}} \mathrm{z} \\ \log _{\mathrm{y}} \mathrm{x} & 1 & \log _{\mathrm{y}} \mathrm{z} \\ \log _{\mathrm{z}} \mathrm{x} & \log _{\mathrm{z}} \mathrm{y} & 1\end{array}\right|\) is equal toKCET 2009 Medium
- The total number of terms in the expansion of \((x+y)^{100}+(x-y)^{100}\) after simplification isKCET 2009 Easy
- If \(\mathbf{a}\) is a vector perpendicular to both \(\mathbf{b}\) and \(\mathbf{c}\), thenKCET 2013 Easy
- If \(f\left(x^{5}\right)=5 x^{3}\), then \(f^{\prime}(x)\) is equal toKCET 2008 Medium
- The negation of the statement " \( 72 \) is divisible by \( 2 \) and \( 3 \) " isKCET 2018 Medium
More PYQs from KCET
- The constant term of the polynomial \(\left|\begin{array}{ccc}x+3 & x & x+2 \\ x & x+1 & x-1 \\ x+2 & 2 x & 3 x+1\end{array}\right|\) isKCET 2010 Medium
- Which one of the following conversions involve change in both hybridisation and shape?KCET 2010 Easy
- A particle moves along the curve \(\frac{x^2}{16}+\frac{y^2}{4}=1\). When the rate of change of abscissa is 4 times that of its ordinate, then the quadrant in which the particle lies isKCET 2023 Easy
- Calculate the cardiac of an individual having 70 heart beats/min with a stroke volume of 55 mL.KCET 2021 Easy
- On bombarding \(\mathrm{U}^{235}\) by slow neutron, \(200 \mathrm{MeV}\) energy is released. If the power output of atomic reactor is \(1.6 \mathrm{MW}\), then the rate of fission will beKCET 2008 Medium
- The electronic conductance depends onKCET 2025 Easy