A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing t

Question

A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing the principles of projectile motion, he decides to perform a simple experiment at the indoor firing range. The soldier hangs a target a distance of d=106 m from the end of the barrel. The rifle is mounted so that the bullet exits moving horizontally at the same height as the bullseye. After 6 trials, the soldier tabulates the values he measured for the distance, h, from the bullseye to the bullet strike.

Bullet drop, h, in cm:

5.92

7.34

7.25

6.27

7.38

6.07

What is the most accurate muzzle velocity that the soldier can report to his sergeant?

What is the uncertainty in this measurement?

Explanation / Answer

let v be the most accurate muzzel velocity

the distance is d = 106 m

we know that

v^2 - u^2 = 2gd

or v^2 = u^2 + 2gd

or v = (u^2 + 2gd)^1/2

where u = 0 and g = 9.8 m/s^2

according to the uncertanity principle we have

dx x dp = (h/2pi)

where dx is the average value of h and dp is equal to m x v,where m is mass of bullet

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