AP EAMCET · Maths · Application of Derivatives
If the petrol burnt in driving a motor boat varies as the cube of the velocity, then the speed (in \(\mathrm{km} /\) hour) of the boat going against a water flow of \(C \mathrm{kms} /\) hour so that the quantity of petrol burnt is minimum is
- A \(\frac{2 C}{3}\)
- B \(\frac{3 C}{2}\)
- C \(\frac{4 C}{3}\)
- D \(\frac{3 C}{4}\)
Answer & Solution
Correct Answer
(B) \(\frac{3 C}{2}\)
Step-by-step Solution
Detailed explanation
Let \(V>C\) the speed of motor boat, relative to water. In fact, relative to land, the motor boat moves with the speed \(V-C\). The motor boat covers a distance \(S\) in \(\frac{S}{V-C} \mathrm{~h}\) and consumption is \(f(v)=k v^3 \cdot \frac{S}{V-C}\), where \(k\) is a…
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