Question

A football is thrown in a parabolic path. Is there any point at which acceleration is parallel to the velocity?Perpendicular to the velocity?

Answer 1

the object will create an arch shape through the air (a parabola)
at the very peak of the trajectory the velocity is parallel to the earth and hence perpendicular to the acceleration due to gravity

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in a physics world there is no place that the velocity is parallel to the acceleration due to gravity this is because we negate air resistance

although if angle theta = 90 degrees (it was thrown straight up) then the object would always have a velocity parallel to the acceleration due to gravity

although because air resistance does exist then towards the end of the path of trajectory the object would be falling vertically down, and hence the velocity is toward the earth, parallel to the acceleration due to gravity

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remember: velocity is the direction of speed, so basically what ever way the object is traveling at an instance in time.

also acceleration only occurs through a force being acted on object, therefore once the object has been thrown the only force and hence acceleration occurring is due to gravity (and air resistance)