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

Question

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