A projectile is thrown at an angle of 30° – what is its motion and range?

A projectile thrown at an angle of 30° follows a parabolic path due to gravity.

The motion can be divided into two components. The horizontal motion has a constant velocity equal to u cos 30°, while the vertical motion is affected by gravity with acceleration g.

The range of the projectile is given by the formula:

R = (u² sin 2θ) / g

For θ = 30°:

R = (u² sin 60°) / g

Since sin 60° = √3/2:

R = (u² √3) / (2g)

Key points:

• The trajectory is parabolic and symmetric.
• Horizontal velocity remains constant.
• Vertical velocity changes due to gravity.
• The range at 30° is less than the maximum range, which occurs at 45°.