Question

You buy a plastic dart gun, and being a clever physics student you decide to do a quick calculation to find its maximum horizontal range. You shoot the gun straight up, and it takes 4.1 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

Answer 1

Have you attempted to use the motion formulas?
You might notice that:
To find max. hor. distance, you'll need velocity and time.
To find the velocity, you'll need time and acceleration.
I'll give a short example on finding the initial velocity of the bullet just exiting the gun barrel.
by using
\[v = u+at\]
where v=0 at the top,
a=-10(gravitational acceleration is different in direction than the initial veloicty),
t is given,
\[0=u-10(4.1)\]
\[u=41ms^{-1}\]
A similar case follows the horizontal distance.