What are the velocity and the acceleration of a projectile thrown at an angle above the horizontal when it reaches its maximum height?

Question

shane_b · Answer

I'm assuming drag is being ignored which is typical for these types of questions.  For both velocity and acceleration there are two components to consider: horizontal and vertical.  

Horizontal velocity will remain constant through the flight since there are no forces acting on it (ignoring drag of course) once it's launched.  Since the horizontal velocity is constant, the horizontal acceleration (dV/dT) must be 0 also.

Vertical velocity is a different story because the force of gravity is involved.  This force acts on the object throughout the flight and is essentially constant (unless you throw it VERY VERY high).  At the top of the flight, the vertical velocity must be 0 because it is changing directions at that point.  Again, the only acceleration in the vertical direction is that of gravity which is constant the entire time (-9.8 m/s^2).

shane_b · Answer

I guess since the question states that it was "thrown" VERY VERY high should really mean impossibly high.  You can can't throw it high enough to reach a point where the acceleration due to gravity will vary.

lgbasallote · Answer

i dont get why @Shane_B made it complicated...the way i understood this..it's just asking the velocity and acceleration at the instant it reaches *maximum height*..which in terms of velocity is 0 m/s because when it reaches the top, then the object will stop for a moment before falling. and acceleration is 9.8 m/s^2 because of gravity. 

why the long paragraph o.O lol

anonymous · Answer

Because the horizontal velocity is not zero at the apex of the trajectory, and the horizontal acceleration is zero only if we neglect friction with the air.

shane_b · Answer

Stop complaining and go back to the math section! :) 

It's not a complicated answer at all but I did want to explain it fully. As Carl_Pham said, the the velocity is NOT 0 m/s at the apex....one component of it is but the other is not. If I just said it was 0m/s then technically my answer would have been wrong.

lgbasallote · Answer

heh that's why i hate math and physics..too choosy and precise :p lol

anonymous · Answer

You LIKE things imprecise?  Goodness, I hope you don't go into brain surgery or ever run a major bank.

shane_b · Answer

I doubt he could do worse than those running the major banks already :)

anonymous · Answer

Hilliard's Infinite Entropy Corollary to Murphy's Law is that things can always get worse.