[Monox D. I-Fly (OP)]

Something was thrown with an elevation angle 60^o. Determine its velocity and direction after:
a. second
b. second

I tried solving the (a) question by substituting the angle to the equation and got 0 (the book uses as the gravity acceleration), which is impossible since at speed 0 the thing must have been stopped, but when I determined the time when it reached the maximum distance using the formula I got second which means the thing hasn't stopped yet in second. Did I make a mistake somewhere?

[Colin2B]

I can’t see your gifs!
Is this a homework question 

[jeffreyH]

Did you use Tex? If so this happens when the latex processor can't understand something or just bombs out.

[jeffreyH]

Alternatively you can generate your gifs here.
http://latex.codecogs.com/eqneditor/editor.php?mode=NEW
Then add them as attachments.

[Monox D. I-Fly (OP)]

I can’t see your gifs!
Is this a homework question 

Not exactly. I am working in a publisher to write some student's worksheets and encountered this question.
What kind of LaTeX does this forum use? What's the HTML tag?

[Colin2B]

[chris]

Better to use the site's in-built latex system (as above) because the generated codes are saved on the site and won't be lost from posts if someone moves or deletes a link...

[Colin2B]

Whoops, my post above ended up in wrong place.
Moved Tex example here.

[Monox D. I-Fly (OP)]

If you quote my post you would see that I have already used the [tex] tag for no result.

[Colin2B]

I’ve had a quick look and found one sequence that should work and another that shouldn’t. Will check out allowable code for this site and get back to you.
If i have time I’ll look at the actual formula and see if i can make sense.

[jeffreyH]

I have tried adjusting the latex in the first post but it won't have it. Very strange!

[Colin2B]

Same here, I’ve cut out odd bits and they check out, but fail here. Hence my question on mod board. Would be good to get to bottom of this.

[Colin2B]

OK, ignoring tex problem and unpicking your question

Something was thrown with an elevation angle . Determine its velocity and direction after:

Question is asking for velocity and direction so you are looking for the vector at time t.
Vector components are Vy=Vy₀sin60 and Vx=Vx₀cos60 where Vy₀ and Vx₀ are x&y components of the starting vector at t=0 - note sin60=√3/2 and cos60=1/2
Vx is constant (ignoring drag) and Vy = Vy₀-gt so at any time you can work out the velocity vector from the components

when I determined the time when it reached the maximum distance .......which means the thing hasn't stopped yet .... Did I make a mistake somewhere?

At max distance you wouldn't expect it to have stopped, it will try and dig a hole in the ground.

[jeffreyH]

Ultimately, maximum distance would be exactly at the centre of gravity of the earth which would be impossible to achieve. Unless the object is traveling in an internal cavity around the centre of mass point. Also impossible to achieve with the earth as the source of the gravitational field. Before settling the object would oscillate across the centre of mass. This object would also be radiating both electromagnetic and gravitational waves. Thus losing kinetic energy over time.

[Colin2B]

Thanks to some sterling work by @chris and @CliffordK the tex is now working.

I assume you have seen my reply https://www.thenakedscientists.com/forum/index.php?topic=72552.msg536177#msg536177

The formula you use in you OP y= only gives you the vertical distance travelled in time t, not the velocity vector at that point.

Just an editorial point. Saying “velocity and direction” is tautological because velocity includes a direction, speed and direction would be better or just ask for the velocity.