A guided missile is fired to strike an object at the same level 38 km away. It may be assumed that it rises vertically 1.5 km and then for the remainder of the flight it follows a parabolic path at an

Question

A guided missile is fired to strike an object at the same level 38 km away. It may be assumed that it rises vertically 1.5 km and then for the remainder of the flight it follows a parabolic path at an elevation of 4 5 ∘ . Calculate its velocity at the beginning of its parabolic path.

TestHub · Accepted Answer

From height h = 1.5 km at 45° elevation, the parabola must cover x = 38 km and land 1.5 km below: t = v c o s 4 5 ∘ x ​ , and − h = x − 2 1 ​ g t 2 (since v sin 4 5 ∘ t = x ). So 2 1 ​ g t 2 = x + h = 39.5 km with t 2 = v 2 2 x 2 ​ : v 2 = x + h g x 2 ​ = 39.5 0.01 × 1444 ​ = 0.3656 in k m 2 / s 2 ( g = 10 m / s 2 = 0.01 km / s 2 ) , v = 0.6047 km / s = 2177 km / h . Matches the printed answer.

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