A spring-loaded gun can fire a projectile to a height h if it is fired straight up. If the same gun is pointed at an angle of 45° from the vertical, what maximum height can now be reached by the projectile?
Correct answer: C. h/2
- A. h/4
- B. h/2√2
- C. h/2
- D. h/√2
Explanation
When the projectile is fired straight up, all of its initial velocity contributes to reaching the height h. At an angle of 45°, only the vertical component of the velocity (v_y = v * sin(45°)) contributes to the maximum height. Since sin(45°) = 1/√2, the vertical component becomes v/√2. Using the formula for maximum height, (v_y^2)/2g, and substituting v_y with v/√2, the height becomes (v^2/2g) * (1/2) = h/2. Thus, the correct answer is h/2. Other options incorrectly modify the vertical component or misapply the trigonometric relationships.
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