A missile is projected so as to attain its maximum range. Calculate the maximum height attained if the initial velocity of projection is 200 ms\(^{-1}\). [g...
Question 1 Report
A missile is projected so as to attain its maximum range. Calculate the maximum height attained if the initial velocity of projection is 200 ms\(^{-1}\). [g = 10ms\(^{-2}\)]
Answer Details
Maximum height for maximum range
A projectile attains its maximum range when it is launched at an angle of \(45^{\circ}\) to the horizontal.
Maximum height: \(H = \dfrac{u^{2}\sin^{2}\theta}{2g}\), with \(u = 200\ \text{m s}^{-1}\), \(\theta = 45^{\circ}\), \(g = 10\ \text{m s}^{-2}\).
\(\sin 45^{\circ} = \dfrac{1}{\sqrt{2}}\), so \(\sin^{2}45^{\circ} = 0.5\).
\(H = \dfrac{200^{2}\times 0.5}{2\times 10} = \dfrac{40000\times 0.5}{20} = \dfrac{20000}{20} = 1000\ \text{m}\).
The maximum height attained is 1000 m.
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