Please help me solve the question A soldier is tasked with measuring the muzzle

Question

Please help me solve the 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 = 113m from the end of the barrel. The rifle is moubted so that the bullet exits moving horizontally at the same height as the bulls eye. After 6 trials, the soldier tabulates the values he measured for the distance, h, from the bullseys to teh bullet strike. What is the most accurate muzzle velocity that the soldier can report to his sergeant? What is the uncertaintly in this measurement?

Explanation / Answer

(a) The average drop h is given by

h = (6.14 + 7.23 + 7.25 + 6.05 + 7.16 + 6.07) / 6

h = 6.65 cm = 0.0665 m

considering motion in vertical direction

h = (1/2)gt2

0.0665 = (1/2) (9.8) t2

t = 0.1165 s

where t is the time of drop.

considering horizontal motion

d = vt

113 = v (0.1165)

muzzle velocity v = 969.96 m/s

(B) For this part we will make above calculations for the lowest and highest values of h

for h = 6.05cm = 0.0605m, performing above calculations we get t=0.1111s and v = 1017.10m/s

for h = 7.25cm = 0.0725m, performing above calculations we get t=0.1216s and v=929.28m/s

difference of two velocities from the calculated one

p1=1017.10-969.96 = 47.14 m/s

p2=969.96-929.28 = 40.68 m/s

Uncertainty in this measurement = (p1+p2)/2 = (47.14 + 40.68 )/2

Uncertainty in this measurement = +/- 43.91 m/s

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