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=103 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: 6.14, 7.23, 7.47, 6.27, 7.38, 6.18 What is the most accurate muzzle velocity that the soldier can report to his sergeant? What is the uncertainty in this measurement?

Explanation / Answer

From each drop, we can calculate the time of travel

Apply d = vot + .5at^2

.0614 = (0) + (.5)(9.8)(t)^2

t = .1119 sec

Then d = vt for the muzzle velocity

103 = v(.1119)

v = 920 m/s

Do this for each value of h

For 7.23 cm

.0723 = (0) + (.5)(9.8)(t^2)

t = .1215 sec

103 = (v)(.1215)

v = 847.9 m/s

The results for the rest are as follows...

For 7.47 cm, t = .1235 sec and v = 834.2 m/s

For 6.27 cm, t = .1131 sec and v = 910.5 m/s

For 7.38 cm, t = .1227 sec and v = 839.3 m/s

For 6.18 cm, t = .1123 sec and v = 917.2 m/s

The average value for the muzzle velocity is

(920 + 847.9 + 834.2 + 910.5 + 839.3 + 917.2)/6

v = 878.2

The uncertainty is + or - 44 m/s

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