Question

A soccer ball is launched with a certain speed from the ground into the air at an angle of 10.6° above the horizontal and lands back on the ground on a target.

What is the other angle that the soccer ball could be launched from the ground with the same speed and hit the same target?

Answer 1

The soccer ball could also be launched at a 79.4° angle above the horizontal with the same speed to hit the same target, due to the symmetry in projectile motion trajectories.

Step-by-step explanation:

The other angle from which a soccer ball could be launched with the same speed to hit the same target on the ground, considering it was initially launched at an angle of 10.6° above the horizontal, can be found using the concept of projectile motion.

Due to the symmetry of projectile trajectories, if launched at the same speed but with different angles, there are always two angles that will result in the same range—one smaller and one larger. To find the second angle, we use the equation θ2 = 90° - θ1, where θ1 is the initial angle of launch (10.6° in this case).

Applying this formula, the second angle is

θ2 = 90° - 10.6° = 79.4°.

Therefore, the soccer ball can also be launched at a 79.4° angle above the horizontal to hit the same target on the ground with the same launching speed.