The horizontal range is four times the maximum height attained by a projectile. The angle of projection is:A 90° B 60° C 45° D 30°
Question
The horizontal range is four times the maximum height attained by a projectile. The angle of projection is:
- A 90°
- B 60°
- C 45°
- D 30°
Solution
The range (R) of a projectile is given by the formula:
R = (v²sin(2θ))/g
where: v is the initial velocity, θ is the angle of projection, and g is the acceleration due to gravity.
The maximum height (H) a projectile can reach is given by the formula:
H = (v²sin²θ)/(2g)
The problem states that the range is four times the maximum height, so we can set up the equation:
R = 4H
Substituting the formulas for R and H gives us:
(v²sin(2θ))/g = 4 * (v²sin²θ)/(2g)
Solving this equation for θ gives us θ = 30°. So, the correct answer is D. 30°.
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