Answer to Question #92294 in Physics for Casey

Question

I have a physics assignment. A spherical ball was launched at an angle of 70 degrees and 20 degrees. These are 2 complementary angles; however, the distances that the balls traveled were very different. One was 2 metres and the other was 1.2 metres. Why are the displacements different despite these being complementary angles? shouldn't they be the same? Keep in mind, the experiments were recorded on the same day, and they were recorded in a room.

Thank you

Answer 1

A flight range of a body thrown at the angle $\alpha$ to the horizontal with a velocity $v$ is $L=\frac{v^2\sin 2\alpha}{g}$. It follows from this formula that if two angles $\alpha$ and $\beta$ are complementary (i.e. $\alpha+\beta=\frac{\pi}{2}$) then flight ranges would be equal if initial velocities are equal.

In the case concerned a ball was thrown at two complementary angles and the flight ranges were different. So it can be explained as that initial velocities were different.