A high-powered rifle fires a bullet with a muzzle speed of0.900 km/s. The gun is

Question

A high-powered rifle fires a bullet with a muzzle speed of0.900 km/s. The gun is pointedhorizontally at a large bull's eye target -- a set of concentricrings -- 175 m away.

(a) How far below the extended axis of the rifle barrel does abullet hit the target? The rifle is equipped with a telescopicsight. It is "sighted in" by adjusting the axis of the telescope sothat it points precisely at the location where the bullet hits thetarget at 175 m.

(b) Find the angle between the telescope axis and the rifle barrelaxis.

When shooting at a target at a distance other than 175 m, the marksman uses the telescopic sight, placingits crosshairs to "aim high" or "aim low" to compensate for thedifferent range. Should she aim high or low, and approximately howfar from the bull's eye should she aim, when the target is at thefollowing distances? Note: The trajectory of the bullet everywhereis so nearly horizontal that it is a good approximation to modelthe bullet as fired horizontally in each case.

(c) 52.5 m by _____ cm?

Explanation / Answer

a) time for bullet to reach target t = 175 / 900 = .1944sec     distance bullet falls s1 = 1/2 g t2 = .185 m = 18.5 cm b) tan = .185 / 175 = 1.057 * 10E-3 rad = .0606deg     this is the angle of thetelescope below that of the rifle barrel c) time for bullet to travel 52.5 m = 52.5 / 900 = .05833sec     distance bullet falls s = 1/2g t2 = .01667 m = 1.667 cm     distance rifle aimed above targeth = 52.5 tan = 52.5 * 1.0586 * 10E-3 = .0555m = 5.56cm     so the rifle should be aimed 5.56 - 1.67 =3.89 cm below the target

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