Maximum Range With Air Resistance

## Question:

I have a question regarding projectiles. I know that
a 45 degree angle produces the maxium distance if air
restistance is neglected. Is the angle for maxium
distance the same, less, or greater than 45 degrees if
air restistance is accounted for.
## Answer:

Air resistance for a non-rotating spherical object affects both horizontal
and vertical components of the object's trajectory in the same way. The
force opposing the motion is proportional to the square of the speed. Since
gravity brings the speed in the vertical direction to zero at some point in
the flight, the horizontal average speed tends to be faster than the
vertical and air resistance therefore has a larger effect on the horizontal
motion. The result of this is that the trajectory is no longer symmetrical
about its highest point, as it was in the no air resistance case. The
descending portion of the trajectory will be cover less ground then the
ascending part, making the angle at which the object hits the ground greater
than the angle of the shot. The maximum range will occur when the sum of
the firing angle and the impact angle are 90 degrees so the firing angle
must be reduced from 45 to achieve maximum range.
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