Question

multiple-choice question the answers are as the angle increases from 45 degrees to 60 degrees, the horizontal distance decreases, and the time in the air increases. as the angle increases from 45 degrees to 60 degrees, the horizontal distance increases, and the time in the air decreases. as the angle increases from 45 degrees to 60 degrees, the horizontal distance increases, and the time in the air increases.

Explanation:

To solve this, we analyze projectile motion:

Key Concepts:

• Time of flight (\( T \)) for a projectile launched with initial speed \( v \) at angle \( \theta \) (from horizontal) is given by \( T = \frac{2v\sin\theta}{g} \) (where \( g \) is gravity). As \( \theta \) increases (from \( 45^\circ \) to \( 60^\circ \)), \( \sin\theta \) increases (since \( \sin45^\circ \approx 0.707 \), \( \sin60^\circ \approx 0.866 \)), so \( T \) increases.
• Horizontal range (\( R \)) is given by \( R = \frac{v^2\sin2\theta}{g} \). For \( \theta = 45^\circ \), \( \sin(2\theta) = \sin90^\circ = 1 \) (maximum range). For \( \theta = 60^\circ \), \( 2\theta = 120^\circ \), and \( \sin120^\circ = \sin(60^\circ) \approx 0.866 \), which is less than \( \sin90^\circ \). Thus, as \( \theta \) increases from \( 45^\circ \) to \( 60^\circ \), \( \sin2\theta \) decreases, so horizontal distance (\( R \)) decreases.

Evaluating the Options:

1. "as the angle increases from 45 degrees to 60 degrees, the horizontal distance decreases, and the time in the air increases." → Matches our analysis (range decreases, time increases).
2. "as the angle increases from 45 degrees to 60 degrees, the horizontal distance increases, and the time in the air decreases." → Incorrect (range decreases, time increases).
3. "as the angle increases from 45 degrees to 60 degrees, the horizontal distance increases, and the time in the air increases." → Incorrect (range decreases).

Answer:

The correct option is:

• as the angle increases from 45 degrees to 60 degrees, the horizontal distance decreases, and the time in the air increases.