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A projectile is aimed at a mark on a horizontal plane through the point of projection and falls 6m short when elevation angle is 30°. The projectile overshoot the mark by 9m when angle of projection is 45°. The correct distance of the mark is ?

A projectile is aimed at a mark on a horizontal plane through the point of projection and falls 6m short when elevation angle is 30°. The projectile overshoot the mark by 9m when angle of projection is 45°. The correct distance of the mark is ?

Grade:11

1 Answers

Shaswata Biswas
132 Points
7 years ago
Let the velocity of projection be u. Distance of mark from point of projection is x.
When angle of projection is 30০ :
Horizontal range = x - 6
\implies \frac{u^{2}sin2*30^{o}}{g} = x - 6           ....... (1)
When the angle of projection is 45০ :
Horizontal range = x + 9
\implies \frac{u^{2}sin2*45^{o}}{g} = x + 9            .........  (2)
(1)÷(2)
\frac{sin60^{o}}{sin90^{o}} = \frac{x -6}{x+9}
\implies x = \frac{9\sqrt{3}+12}{2-\sqrt{3}}

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