Question

there is a minimum angle above the ground such that if the ball is launched below this angle, it can never clear the bar, no matter how fast it is kicked. what is this angle?

Answer 1

The minimum angle to clear a bar with a projectile varies and is greater than 0° but less than the angle for maximum range, which is 45° in vacuum conditions. It depends on the initial speed of the ball and the distance to the bar.

Step-by-step explanation:

The question revolves around the concept of projectile motion in physics, specifically the minimum launch angle needed to clear a bar.

In the context of projectile motion without air resistance, we know that the maximum range for a projectile on level ground is obtained when the launch angle is 45°.

It's mentioned that the range is maximum at 45°, and for two initial launch angles that sum up to 90°, the projectiles will have the same range.

This implies that there is no single minimum angle to clear a bar under all circumstances, as it depends on the initial speed of the projectile (ball in this case) and the distance to the bar.

However, if the bar's height is not negligible, a certain minimum angle would indeed be required to clear it which will be greater than 0°, and less than the angle that yields the maximum range at the given initial speed.