# What is the maximum horizontal range of your gun?

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 2.8 s for the dart to land back at the barrel. What is the maximum horizontal range of your gun?

2.8 secs for up and down motion.
1.4 sec s for up motion only.
v = u+at. For the vertical upward motion, the equation is modified as
0=u-gt = u-g*1.4
u = 9.8*1.4 = 13.72 m/sec
With this velocity, we shoot the gun at an angle Θ above horizintal.
The max horizontal range of the gun occurs when Θ=45 deg.
It is equal to u^2/(g) = 13.72^2 /(9.8) m
=19.208 meters.

Plastic Dart Gun

Gravity – -9.8 m/s^2

time = 2.8s full flight, so it takes 1.4 s to reach the apex of the flight.

so the initial velocity of the dart is (1.4s)(9.8m/s^2) = 13.72m/s

We know that greatest distance that can be achieved by a prjectile occurs when it is fired at 45 degree angle.

So we have to resolve the vertical and horizontal velocities when fired at a 45 degree angle.

So we can use pyhtagorean theorem to figure out he other two sides

h^2 = o^2+a^2
o=a
h^2=2a^2
h=root(2)a

a=o=h/root(2)=13.72/root(2)=9.701

so it will fly for 9.701/9.8 seconds = .99 sec

.99s*9.701m/s = 9.6 m

It will fly 9.6 m. (31.5 feet)

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