Question

Taylor is interested in archery. She draws her bow and shoots an arrow at an angle of 50º. It goes a distance of 100 meters. At what other angle could Taylor shoot an arrow with the same amount of force and have it go the same distance?

Answer 1

40° to get the same range if one angle of projection is Θ then other is 90-Θ As R=u²sin2Θ/g sin2Θ =sin 2 (90-Θ) =sin (180-2Θ ) =sin 2Θ {as sin 180-Θ=sin Θ }

Answer 2

Range of a projectile depends on the the velocity and the angle of projection.
If Taylor shoots an arrow with came amount of force, then its velocity will be the same as earlier. To get the same range 100m, he could shoot at the complementary angle of earlier projectile.
He had shot at 50 degree. So he can shoot at (90-50=40 degree) to get the same range 100m.