Neep help setting up an equation...

[teany]

Hey guys! I don't really understand this question and the worked solutions dont make much sense to me either... its from MAV 2007 multiple choice

A bullet of mass m kg is shot vertically up with an initial speed of 400 m/s. It is subjected to an air resistance of (mv^2)/1000 newton where v m/s is the speed of the bullet. The maximum height that the bullet reaches is...

So do you use F=ma or...?

Thanks in advance! I get the working out, but I just don't get how you get the equation!

[SocialRhubarb]

Yep, just use F=ma, remembering to account for both air resistance and the bullet's weight force.

[b^3]

Remember we have , so we need to look at the forces acting on the bullet. The bullet is travelling upwards, but it's weight force is acting in the opposite direction to it's direction of motion, and secondly we have air resistance, which again since it's acting downwards is acting in the opposite direction to it's direction of motion. Lets make upwards as positive, then we have the situation below.

Now heres where they've made a mistake in the solutions, the first equals sign should be a negative, so you should have
.
So basically adding up the forces we have to get the net force, then letting that equal .
Then from there on they should be correct.

EDIT: Beaten.

[teany]

Ohhh thank you both! I didnt even think about the weight force... and thanks b^3 for the diagram that really clears things up