Brandon launches a projectile at an angle of 75 degrees above the horizontal, which strikes the ground a certain distance down range. For what other angle of launch at the same speed would the projectile land just as far away?
To find the angle of launch at the same speed that would make the projectile land just as far away, we can use the principle of symmetry in projectile motion.
When a projectile is launched with an initial angle θ above the horizontal, the range (horizontal distance covered) depends on both the initial velocity and the launch angle. However, if the projectile is projected at an angle (90° - θ) below the horizontal, it will follow the same trajectory but symmetrically mirrored. This means that it will cover the same horizontal distance.
In this case, the projectile was launched at an angle of 75° above the horizontal. Therefore, to find the other angle at which the projectile would land just as far away, we subtract the launch angle from 90°:
90° - 75° = 15°
So, if the projectile was launched at an angle of 15° below the horizontal with the same initial speed, it would land just as far away as the original launch angle of 75° above the horizontal.