A rifle is used to shoot twice at a target using identical cartridges. The first

Question

A rifle is used to shoot twice at a target using identical cartridges. The first time, it is aimed parallel to the ground and directly at the center of the bull's eye. The bullet strikes the target at a distance of HA below the center, however. The second time, the rifle is similarly aimed, but from 3.28 times the distance from the target. This time the bullet strikes the target at a distance of HB below the center. Find the ratio HB/HA.

Explanation / Answer

->for vertical displacement: y = -0.5*g*t^2 ->for horizontal displacement: x = vx*t Eliminating 't' from both eqns, we get: y = -0.5*g*(x/vx)^2 Assuming vx the horizontal component of velocity is constant, y = { -0.5*g/vx^2 }*(x^2) y is directly proportional to x^2 let y1 = Ha (depth of the first shot) y2 = Hb (depth of the second shot) Hb/Ha = y2/y1 = x2^2 / x1^2 = (x2/x1)^2 = (3.37*x1/x1)^2 = 11.35 Hence ratio of Hb to Ha equals 11.35

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