At what angle from the ground should a projectile be launched to achieve maximum range?

At what angle from the ground should a projectile be launched to achieve maximum range?

• A. 0°
• B. 45°
• C. 60°
• D. 90°

Answer: (B)

To maximize how far a projectile travels horizontally when launched from level ground with a fixed speed and no air resistance, the range depends on the angle. The range can be written as R = v^2 sin(2θ) / g, where v is the launch speed and g is gravity. With the speed fixed, maximizing the range means maximizing sin(2θ). Since sin reaches its maximum value at 1 when 2θ = 90°, the optimal angle is θ = 45°. Intuitively, 45° provides a good balance between vertical lift and forward speed, giving enough time aloft while preserving forward motion. If the ground heights differ or air drag is present, the best angle shifts away from 45°.

To maximize how far a projectile travels horizontally when launched from level ground with a fixed speed and no air resistance, the range depends on the angle. The range can be written as R = v^2 sin(2θ) / g, where v is the launch speed and g is gravity. With the speed fixed, maximizing the range means maximizing sin(2θ). Since sin reaches its maximum value at 1 when 2θ = 90°, the optimal angle is θ = 45°. Intuitively, 45° provides a good balance between vertical lift and forward speed, giving enough time aloft while preserving forward motion. If the ground heights differ or air drag is present, the best angle shifts away from 45°.