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 = 102 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 tor the distance, h, from the bullseye to the bullet strike. What is the most accurate muzzle velocity that the soldier can report to his sergeant? Table 1: Vertical displacement data

Explanation / Answer

let muzzle speed be v m/s.

time taken to travel d meters horizontally =distance/speed

==>t=d/v

in vertical direction, initial speed=0

acceleration=9.8 m/s^2

then distance travelled in t seconds=initial speed*time+0.5*acceleration*time^2

=0.5*9.8*(d/v)^2

=4.9*d^2/v^2

=4.9*102^2/v^2

=50979.6/v^2

==>v=sqrt(50979.6/h)

h (in m)   v (in m/s)
0.0603       919.4742
0.0734       833.3936  
0.0747       826.1101
0.0616       909.7202
0.0727       837.3962
0.0596       924.8581

most accurate value of v will be average of all the 6 readings

=875.1587 m/s

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